TY - JOUR

T1 - On al most recognizability by spectrum of simple classical groups

AU - Staroletov, Alexey

N1 - Publisher Copyright: © 2017 University of Isfahan.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The set of element orders of a finite group G is called the spectrum. Groups with coinciding spectra are said to be isospectral. It is known that if G has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic groups isospectral to G. The situation is quite different if G is a nonabelain simple group. Recently it was proved that if L is a simple classical group of dimension at least 62 and G is a finite group isospectral to L, then up to isomorphism L ≤ G ≤ Aut L. We show that the assertion remains true if 62 is replaced by 38.

AB - The set of element orders of a finite group G is called the spectrum. Groups with coinciding spectra are said to be isospectral. It is known that if G has a nontrivial normal soluble subgroup then there exist infinitely many pairwise non-isomorphic groups isospectral to G. The situation is quite different if G is a nonabelain simple group. Recently it was proved that if L is a simple classical group of dimension at least 62 and G is a finite group isospectral to L, then up to isomorphism L ≤ G ≤ Aut L. We show that the assertion remains true if 62 is replaced by 38.

KW - Almost recognizable group

KW - Element orders

KW - Prime graph of a finite group

KW - Simple classical groups

UR - http://www.scopus.com/inward/record.url?scp=85028457298&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85028457298

VL - 6

SP - 7

EP - 33

JO - International Journal of Group Theory

JF - International Journal of Group Theory

SN - 2251-7650

IS - 4

ER -