in Mathematics -
M.Sc. in Mathematics -
Title of M.Sc. Thesis: Some results and problem arising from a question of Paul Erdos
Supervisor: Prof. A. Mohammadi Hassanabadi
Ph.D. in Mathematics -
Title of Thesis: Some combinatorial conditions on groups
Supervisor of First Ph.D.: Prof. A. Mohammadi Hassanabadi
Second Ph.D. in Mathematics - Universite de Provence, CMI France (October 2000-June 2001)
Title of Thesis: Quelques conditions d'Engel dans certaines classes de groupes.
(In English: Some Engel conditions in certain classes of groups)
Supervisor of Second Ph.D.: Prof. Gerard Endimioni
1. Algebra 1
2. Linear Algebra
3. Advanced Algebra
4. Topics in Group Theory
5. Coding Theory
6. Topics in Ring Theory
7. Graph Theory
8. Algebra 3
1. Combinatorial conditions on finite and infinite subsets of groups and rings
2. Engel elements in groups
3. Non-inner automorphisms of order p in finite p-groups
4. Integral Cayley graphs and one-factorizations in Cayley graphs
5. Non-Commuting graph, non-nilpotent graph, Engel graph, non-cyclic graph of groups
Mathematics Subject Classifications (2000): 20; 16; 05; 20F45; 20D60; 20D45.
AWARDS and Honors:
1. First grade student in B.Sc.
2. First grade student in M.Sc.
3. First grade student in Ph.D.
4. Second prize in Alkharazmi young festival 1999.
5. First prize in Sheikh Bahaei festival 1999.
6. Ten months scholarship from
8. Scholarship from the abdus salam international centre for theoretical physics (ICTP) in Italy-Trieste for passing one month in the centre from 24 July 2003 to 24 August 2003.
9. Awarded to become a Junior Associate of ICTP for the period 2003-2008.
10. Distinguished researcher in basic sciences of the University of Isfahan (2005-2006).
11. Distinguished lecturer of 2006-2007 in Faculty of Sciences in University of Isfahan.
13. Head of distinguished Center of Excellence in Basic Sciences (Selected by Ministry of Science and Education) 1388 (2010).
1. Reviewer of Zentralblatt MATH.
2. Reviewer of the American Mathematical Reviews.
5. Referee for
a) Algebra Colloquium. (World Scientific).
b) Journal of Applied Mathematics & Computing. (Korean Society for Computational & Applied Mathematics and the Korean SIGCAM)
c) Communications in Algebra (Taylor & Francis)
d) Far East Journal of Mathematical Sciences (FJMS) (Pushpa Publishing House)
e) Bulletin of the Malaysian Mathematical Sciences Society
f) Linear Algebra and its Applications (Elsevier Inc.)
g) Journal of Sciences, Islamic Republic of Iran (University of Tehran)
h) International Electronic Journal of Algebra (Int. Electron. J. Algebra, Turkey)
i) Utilitas Mathematica (Univ. Natal Dept. Math. Appl. Math. Durban, South Africa)
j) Ars Combinatoria (Charles Babbage Res. Centre, Canada)
k) Journal of Group Theory (Walter de Gruyter)
n) International Journal of Mathematics and Mathematical Sciences (Hindawi Publishing Corporation)
p) Acta Mathematica Sinica (Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, published by Springer)
q) Journal of Algebra (Elsevier Inc.)
r) Bulletin of the Iranian Mathematical Society
s) American Mathematical Monthly
t) Journal of Algebraic Combinatorics (Springer)
Collaboration in Conference Organizing:
1) Member of the Scientific and Administrative Committees of The first Two-Days Group Theory Seminar in IRAN.
2) Member of the Scientific Committee of the 20th Seminar on Algebra of IRAN.
3) Member of the Scientific Committee of The Second Group Theory Conference in IRAN, Mashhad.
4) Member of the Scientific Committee of The Third Conference and Workshop on Group Theory, IRAN, Tehran.
5) Member of the Scientific Committee of The First Biennial International Group Theory Conference 2011, Malaysia, Johor Bahru.
6) Member of the Scientific and Organizing Committee of The Third Algebraic Combinatorics Conference of Iran, 2011, University of Isfahan.
7) Member of the Scientific Committee of The Fourth Group Theory Conference of IRAN, Isfahan Payame Noor University, March 7-9, 2012.
8) Member of the Scientific Committee of The Fifth Group Theory Conference of IRAN, Islamic Azad University, Mashhad- Iran, March 13-15, 2013.
9) Member of the Scientific Committee of The 23th Algebra Seminar of IRAN, Khansar Faculty of Computer and Mathematics, Khansar- Isfahan, Iran, November 21-22, 2013.
10) Member of the Scientific Committee of the 6th National Mathematics Conference of Payam Noor University, Isfahan, Iran, 5-6 March 2014.
11) Member of the Scientific Committee of The Sixth Group Theory Conference of IRAN, Golestan University, Gorgan, March 12-13, 2014.
12)Member of the Scientific Committee of The 7th Group Theory Conference of IRAN and 3rd Biennial International Group Theory Conference, Ferdowsi University of Mashad, Mashhad, 28-31 January, 2015.
13) Member of the Scientific Committee of The 8th Group Theory Conference of IRAN, University of Tabriz, Tabriz, 3-5 February, 2016.
14) Member of the Scientific Committee of The 4th Biennial International Group Theory Conference, Malaysia, Kuala Lumpur, Universiti Teknologi Malaysia, 23-26 January, 2017.
15) Member of the Scientific Committee of The 9th Group Theory Conference of IRAN, University of Kashan, Kashan, 1-3 February, 2016.
Published or Accepted in 2017
97. Alireza Abdollahi and Z. Taheri, Zero divisors and units with small supports in group algebras of torsion-free groups, to appear in Communications in Algebra. [PDF]
96. Alireza Abdollahi, M. Arezoomand, Finite nilpotent groups that coincide with their 2-closures in all of their faithful permutation representations, to appear in Journal of Algebra and Its Applications. [PDF]
95. Alireza Abdollahi, M. Ghuedri and Y. Guerboussa, Non-triviality of Tate cohomology for certain classes of finite p-groups, to appear in Communications in Algebra. [PDF]
94. Alireza Abdollahi, M. Jazaeri and Edwin R. van Dam, Distance-regular Cayley graphs with least eigenvalue -2, Designs, Codes and Cryptography, 84 No. 1 (2017) 73-85. [PDF]
93. Alireza Abdollahi, S. M. Ghoraishi and M. Ahmadi, Finite p-groups with the least number of outer p-automorphisms, Journal of Algebra and Its Applications, Vol. 16, No. 5 (2017) 1750111 (12 pages). [PDF]
92. Alireza Abdollahi and S. M. Ghoraishi, On noninner automorphisms of 2-generator finite p-groups, Comm. Algebra, Vol. 45, No. 8 (2017) 3636-3642. [PDF]
91. Alireza Abdollahi, Sh. Janbaz and M Ghahramani, A large family of cospectral Cayley graphs over dihedral groups, Discrete Mathematics, Vol. 340 (2017) 1116-1121. [PDF]
Published or Accepted in 2016
90. Alireza Abdollahi and M. Jazaeri, Integral graphs with distinct eigenvalues, to appear in Ars Combinatoria. [PDF]
89. Alireza Abdollahi, Sh. Janbaz and M. Jazaeri, Groups all of whose undirected Cayley graphs are determined by their spectra, Journal of Algebra and Its Applications, Vol. 15, No. 9 (2016) 1650175 (15 pages) . [PDF]
88. Alireza Abdollahi and Amir Loghman, Cayley graphs isomorphic to the product of two Cayley graphs, Ars Combinatoria, 126 (2016) 301-310. [PDF]
Published or Accepted in 2015
87. Alireza Abdollahi and H. Mousavi, Finite nilpotent groups whose cyclic subgroups are TI-subgroups, to appear in Bull. Malays. Math. Sci. Soc. [PDF]
86. Alireza Abdollahi and M. Zallaghi, Character sums for Cayley graphs, Comm. Algebra, 43 (2015) 5159-5167. [PDF]
85. Alireza Abdollahi, Sh. Janbaz and M. R. Oboudi, Distance between spectra of graphs, Linear Algebra and its Applications, Vol. 466 (2015) 401-408. [PDF]
84. Alireza Abdollahi, Non-solvable groups generated by involutions in which every involution is left 2-Engel, Journal of Group Theory, Vol. 18 No. 1 (2015) 111-114. [PDF]
Published or Accepted in 2014
83. A. Tavakoli, A. Rejali, A. Yousofzadeh and Alireza Abdollahi, A note about configuration of a group, MATEMATIKA, Vol. 30, No. 2 (2014) 117-121. [PDF]
82. Alireza Abdollahi, Sh. Janbaz and M. R. Oboudi, Cospectrality measures of graphs with at most six vertices, Journal of Algebraic Structures and their Applications, Vol. 1 No. 1 (2014) 57-67. [PDF]
81. Alireza Abdollahi and S. M. Ghoraishi, p-Groups for which each outer p-automorphism centralizes only p elements, Glasnik Matematicki Vol. 49(69) (2014) 119 -122 [PDF]
80. Alireza Abdollahi and Shahrooz Janbaz, Connected graphs cospectral with a Friendship graph, Trans. Comb., 3 No. 2 (2014) 17-20. [PDF]
79. Alireza Abdollahi and Mohammad Reza Oboudi, Cospectrality of graphs, Linear Algebra and its Applications, 451 (2014) 169-181. [PDF]
78. Alireza Abdollahi, S. M. Ghoraishi, Y. Guerboussa, M. Reguiat and B. Wilkens, Noninner automorphisms of order p for finite p-groups of coclass 2, Journal of Group Theory, 17 (2014) 267-272. [PDF]
77. Alireza Abdollahi and S. M. Ghoraishi, On noninner 2-automorphisms of finite 2-groups, Bulletin of the Australian Mathematical Society, 90 No. 2 (2014) 227-231. [PDF]
76. Alireza Abdollahi and M. Jazaeri, Groups all of whose undirected Cayley graphs are integral, European Journal of Combinatorics 38 (2014) 102-109. [PDF]
75. Alireza Abdollahi, Groups with maximal irredundant covers and minimal blocking sets, Ars Combinatoria 113 (2014) 337-339.[PDF]
74. Alireza Abdollahi and Hamid Shahverdi, Non-commuting graphs of nilpotent groups, Communications in Algebra 49 No. 9 (2014) 3944-3949. [PDF]
Published in 2013
73. Alireza Abdollahi, Shahrooz Janbaz and Mohammad Reza Oboudi, Graphs cospectral with a friendship graph or its complement, Trans. Comb., 2 No. 4 (2013) 37-52. [PDF]
72. Alireza Abdollahi and S. M. Ghoraishi, Noninner automorphisms of finite p-groups leaving the center elementwise fixed, Int. J. Group Theory, 2 no. 4 (2013) 17-20. [PDF]
70. Alireza Abdollahi and M. Jazaeri, On groups admitting no integral Cayley graphs besides complete multipartite graphs, Appl. Anal. Discrete Math. 7 (2013), 119-128. [PDF]
69. Alireza Abdollahi, S. Akbari, H. Dorbidi and H. Shahverdi, Commutativity pattern of finite non-abelian p-groups determine their orders, Communications in Algebra, 41 No. 2 (2013) 451-461. [PDF]
68. Alireza Abdollahi and A. Loghman, On one-factorizations of replacement products, Filomat, 27: 1 (2013) 57-63. [PDF]
Published in 2012
67. Alireza Abdollahi, Determinants of adjacency matrices of graphs, Trans. Comb. 1 No. 4 (2012) 9-16. [PDF]
66. Alireza Abdollahi and H. Shahverdi, Characterization of the alternating group by its non-commuting graph, Journal of Algebra, 357 (2012) 203-207. [PDF]
64. A. Tavakoli, Alireza Abdollahi, H.E. Bell, Rings with a setwise polynomial-like condition, Bulletin of the Iranian Mathematical Society 38 No. 2 (2012) 305-311. [PDF]
Published or Accepted in 2011
63. Alireza Abdollahi , R. Brandl and A. Tortora, Groups generated by a finite Engel set, Journal of Algebra 347 (2011) 53-59. [PDF]
64. Alireza Abdollahi and Francesco G. Russo, On a problem of P. Hall for Engel words, Arch. Math. (Basel) 97 (2011) 407-412. [PDF]
62. Alireza Abdollahi, Cohomologically trivial modules over finite groups of prime power order, Journal of Algebra 342 (2011) 154-160. [PDF]
61. Alireza Abdollahi and E. Vatandoost, Integral quartic Cayley graphs of abelian groups, The Electronic Journal of Combinatorics 18 (2011), #P89.[PDF]
60. Alireza Abdollahi, Engel elements in groups, London Mathematical Society Lecture Note Series: 387, Groups St Andrews 2009 in
Bath , Volume 1, Cambridge University Press, 2011, pp. 94-117. [PDF]
Published or Accepted in 2010
59. Alireza Abdollahi, A. Faghihi, S.A. Linton and E.A. O'Brien, Finite 3-groups of class 3 whose elements commute with their automorphic images, Arch. Math. (Basel) 95 No.1 (2010) 1-7. [PDF]
58. Alireza Abdollahi and H. Khosravi, Right 4-Engel elements of a group, Journal of Algebra and Its Applications 9 (2010) 763-769. [PDF]
57. Alireza Abdollahi, Powerful p-groups have noninner automorphisms of order p and some cohomology, Journal of Algebra 323 (2010) 779-789. [PDF]
56. Alireza Abdollahi and H. Khosravi, On the right and left 4-Engel elements, Communications in Algebra 38 No. 3 (2010) 933-943. [PDF]
55. Alireza Abdollahi, A. Azad, A. Mohammadi Hassanabadi and M. Zarrin, On the clique number of non-commuting graphs of certain groups, Algebra Colloquium 17 No. 4 (2010) 611-620. [PDF]
54. Alireza Abdollahi and M. Zarrin, Non-nilpotent graph of a group, Communications in Algebra , 38 No. 12 (2010) 4390-4403. [PDF]
Published or Accepted in 2009
53. Alireza Abdollahi and E. Vatandoost, Which Cayley graphs are integral?, The Electronic Journal of Combinatorics 16 (2009), #R122. [PDF]
52. Alireza Abdollahi and A. Mohammadi Hassanabadi, Non-cyclic graph associated with a group, Journal of Algebra and Its Applications, 8 No. 2 (2009) 243-257. [PDF]
51. Alireza Abdollahi and A. Tavakoli, A note on centrality in infinite groups, Southeast Asian Bulletin of Mathematics, 33 (2009) 207-208. [PDF]
49. Alireza Abdollahi, A. Rejali and A. Yousofzadeh, Configuration of nilpotent groups and isomorphism, Journal of Algebra and Its Applications 8, No. 3 (2009) 339-350. [PDF]
48. Alireza Abdollahi, Characterization of SL(2,q) by its non-commuting graph, Beitrage zur Algebra und Geometrie, 50, No. 2, (2009) 443-448.[PDF]
Published or Accepted in 2008
47. Alireza Abdollahi, A. Faghihi and A. Mohammadi Hassanabadi, 3-Generator groups whose elements commute with their endomorphic images are abelian , Communications in Algebra, 36 No. 10 (2008) 3783-3791. [PDF]
46. Alireza Abdollahi, A. Faghihi and A. Mohammadi Hassanabadi, Minimal number of generators and minimum order of a non-Abelian group whose elements commute with their endomorphic images, Communications in Algebra, 36 No. 5 (2008) 1976-1987. [PDF]
44. Alireza Abdollahi, Commuting graphs of full matrix rings over finite fields, Linear Algebra and its Applications, 428 (2008) 2947-2954. [PDF]
43. Alireza Abdollahi, 1-factorizations of Cayley graphs, Ars Combinatoria, 86 (2008) 129-131. [PDF]
42. Alireza Abdollahi and H. R. Maimani, A new technique for constructing pairwise balanced designs from groups, Ars Combinatoria, 86 (2008) 409-413.[PDF]
41. Alireza Abdollahi and S.M. Jafarian Amiri, Minimal coverings of completely reducible groups, Publicationes Mathematicae Debrecen, 72/1-2 (2008), 167-172 . [PDF]
Published in 2007
40. Alireza Abdollahi, Engel graph associated with a group, Journal of Algebra, 318 (2007) 680-691. [PDF]
39. Alireza Abdollahi, H.E. Bell and A.A. Klein, On commutativity and centrality in infinite rings, Communications in Algebra, 35 (2007) 1323-1332. [PDF]
37. Alireza Abdollahi and S.M. Jafarian Amiri, On groups with an irredundant 7-cover, Journal of Pure and Applied Algebra, 209 (2007) 291-300. [PDF]
36. Alireza Abdollahi, S.M. Jafarian Amiri and A. Mohammadi Hassanabadi, Groups with specific number of centralizers, Houston Journal of Mathematics, 33, No. 1 (2007), 43-57 . [PDF]
35. Alireza Abdollahi, Finite p-groups of class 2 have noninner automorphisms of order p, Journal of Algebra, 312 (2007) 876-879. [PDF]
34. Alireza Abdollahi and A. Mohammadi Hassanabadi, Non-cyclic graph of a group, Communications in Algebra, 35 (2007) 2057-2081. [PDF]
33. Alireza Abdollahi, F. Ashraf and S.M. Shaker, The symmetric group of degree six can be covered by 13 and no fewer proper subgroups, Bulletin of the Malaysian Mathematical Sciences Society, Second Series, 30 No. 1 (2007) 57-58. [PDF]
Published in 2006
Published in 2005
28. Alireza Abdollahi, Groupes satisfaisant une condition d'Engel, Journal of
Algbera, 283, No. 2 (2005) 431-446. [PDF]
Published in 2004
22. Alireza Abdollahi, Powers of a product of commutators as products of
squares, International Journal of Mathematics and Mathematical
Sciences, 2004:7 (2004) 373-375. [PDF]
Published in 2003
17. Alireza Abdollahi, Certain locally nilpotent varieties of groups, Bull. Austral. Math. Soc. 67 (2003) 115-119. [PDF]
Published in 2002
16. Alireza Abdollahi, A combinatorial problem in infinite groups, Bull. Malays.
Math. Sci. Soc. (2) 25 (2002) 101-114. [PDF]
9 (2002) 205-215. [PDF]
130 (2002) 2827-2836. [PDF]
Published in 2001
13. Alireza Abdollahi, Some Engel conditions on finite subsets of certain
groups, Houston J. Math. 73 no. 3 (2001) 511-522. [PDF]
Published in 2000
9. Alireza Abdollahi, Infinite groups with an Engel condition on infinite
subsets, Bull. Iranian Math. Soc. 26 no. 1 (2000) 73-78. [PDF]
Published in 1999
5. Alireza Abdollahi, A characterization of infinite 3-abelian groups, Arch.
Published in 1998
1. Alireza Abdollahi and Aliakbar Mohammadi Hassanabadi, A characterization of infinite abelian groups, Bull. Iranian Math. Soc. 24 no. 2
(1998) 41-48. [PDF]
Presentation in Conferences:
1. Alireza Abdollahi, Integral of a group, 29th Iranian International
Conference on Mathematics, Amirkabir University of Technology (Tehran
Polytechnic), Iran, March 28-31, 1998.
3. Alireza Abdollahi, An Engel condition on certain residually finite groups,
30th Iranian International Conference on Mathematics,
7. Alireza Abdollahi and Bijan Taeri, A combinatorial condition on infinite
rings, Proceedings of the 31st Iranian Mathematics Conference, University of
Tehran, Iran, August 27-30, 2000, 23-27.
9. Alireza Abdollahi, 4-Engel groups and certain locally nilpotent varieties
of groups, (Invited Speaker) 14th Iranian Algebra Seminar of Iran, Azzahra
University, Tehran-Iran, July 16-18, 2002.
13. Alireza Abdollahi, Infinite Ramsey's theorem and some of its applications
in group theory, One hour talk delivered at Institute for Studies
in Theoretical Physics and Mathematics (IPM),
Gaveh zang Zanjan, Iran. (This
is an improved version of the Item 3 in 2002, see below.) [PDF]
16. Alireza Abdollahi, Rings in which a given polynomial has many solutions,
35th Annual Iranian Mathematics Conference, Shahid Chamran University of
Ahvaz, January 26-29, 2005. [PDF]
Supervised M.Sc. Students and Title of Their Thesis:
1) A. Mosaiebi, (2001) A combinatorial condition on infinite groups, (Advisor)
2) M. Behdari, (2002) Engel conditions on groups, (Advisor)
3) M. J. Abbasi, (2002) Some combinatorial Engel conditions on groups, (Supervisor)
4) M. Zarrin, (2002) Subnormal conditions on non-torsion groups, (Supervisor)
5) M. Elyasi, (2002) Some combinatorial conditions on groups and applications of Ramsey's theorem, (Supervisor)
6) J. Sarhadi,(2002) Study of subgroups of finite p-groups, (Advisor)
7) S. Afshari, (2002) Study of rewritable groups, (Advisor)
8) P. Rashno, (2002) Characterization of groups in which the product of every four elements is permutable, (Advisor)
9) H. Khosravi, (2003) Engel groups and semigroup laws, (Supervisor)
10) M. Araskhan, (2003) Some bounds for locally nilpotent groups in certain variety of groups, (Supervisor)
11) R. Mohamdpour Nashli, (2003) Semicomplete groups, (Advisor)
12) A. Rahmatimanesh, (2003) Central automorphisms of groups, (Advisor)
13) M. Aminian, (2004) Covering algebras, (Advisor)
14) B. Behzadi Share Babak, (2005) Sequenceablity of groups, (Supervisor)
15) R. Niazi, (2005) 3-rewritable groups, (Advisor)
16) F. Ashraf, (2006) Groups which union of finitely many subgroups, (Supervisor)
17) S. M. Shaker Khovidaki, (2007) Study of coverings of symmetric groups of small degrees, (Supervisor)
18) A. Zeidi, (2008) 9-centralizers groups, (Supervisor)
19) E. Nasibi, (2009) Groups with given central automorphism of groups, (Supervisor)
Click HERE to see supervised Ph.D. Students and Title of their Thesis
Iranian Group Theorists (who I know):
1) Ahmad Erfanian
2) Mohammad Reza Darafsheh
6) H. Doostie
7) Ali Iranmanesh
8) Ali Reza Ashrafi
9) A. Rahnamai Barghi
10) Behrooz Khosravi
11) Mohammad Reza Pournaki
12) Bijan Taeri
13) Ali Reza Moghaddamfar
14) Hamid Mousavi
15) Saeed Kayvanfar
16) Behrooz Mashayekhy
17) Ali Reza Salemkar
18) Houshang Behravesh
19) M. Akhavan Malayeri
20) Z. Mostaghim
21) M. R. Moghaddam
22) A. Azad
23) M. Zarrin
24) A. Faghihi Afarni
25) S. M. Majid Jafarian Amiri
26) M. J. Ataei