Finite groups isospectral to simple groups

Abstract

The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for which the recognition problem is solved.

Numbering of theorems, lemmas and other assertions has been changed to match that of the version published in Commun. Math. Stat

References in corpus (11)

• An adjacency criterion for the prime graph of a finite simple group
• Cocliques of maximal size in the prime graph of a finite simple group
• On finite groups isospectral to simple classical groups
• On the structure of finite groups isospectral to finite simple groups
• On orders of elements of finite almost simple groups with linear or unitary socle
• On element orders in covers of finite simple groups of Lie type
• On the nilpotency of the solvable radical of a finite group isospectral to a simple group
• On recognition of symplectic and orthogonal groups of small dimensions by spectrum
• Almost recognizability by spectrum of simple exceptional groups of Lie type
• On the prime graph of a finite group with unique nonabelian composition factor
• On element orders in covers of $L_4(q)$ and $U_4(q)$

Cited by in corpus (3)

• Criterion of nonsolvability of a finite group and recognition of direct squares of simple groups
• On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups
• On recognition of direct powers of finite simple linear groups by spectrum