On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups

Abstract

The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2-subgroups are considered. It is proved that the direct square $J_1\times J_1$ of the sporadic Janko group $J_1$ and the direct squares ${}^2{G}_2(q)\times {}^2{G}_2(q)$ of the simple small Ree groups ${}^2{G}_2(q)$ are uniquely characterized by their spectra in the class of finite groups, while for the direct square $PS{L}_2(q)\times PS{L}_2(q)$ of a 2-dimensional simple linear group $PS{L}_2(q)$, there are always infinitely many groups (even solvable groups) with the same spectra.

References in corpus (5)

• 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
• Finite groups isospectral to simple groups
• Criterion of nonsolvability of a finite group and recognition of direct squares of simple groups