TY - JOUR
ID - 899
TI - Simple groups with the same prime graph as $D_n(q)$
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Khosravi, B.
AU - Babai, A.
AD - Department of Pure Mathematics, Faculty of Mathematics and Computer Sciences,
Amirkabir University of Technology, 424,
Hafez Ave., Tehran 15914, Iran.
AD - Department of Mathematics, University of Qom, P.O. Box 37185-3766, Qom, Iran.
Y1 - 2016
PY - 2016
VL - 42
IS - 6
SP - 1403
EP - 1427
KW - Prime graph
KW - simple group
KW - Vasil'ev conjecture
DO -
N2 - Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph as an alternating group, Siberian Math. J., 2013] the above conjecture is positively answered when one of these pairwise nonisomorphic groups is an alternating group.In this paper, we continue this work and determine all nonabelian simple groups, which have the same prime graph as the nonabelian simple group $D_n(q)$.
UR - http://bims.iranjournals.ir/article_899.html
L1 - http://bims.iranjournals.ir/article_899_fccfee9cd92567c1b231239ddc9bfa0f.pdf
ER -