Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic~2

A. V. Vasil'ev ; M. A. Grechkoseeva

Algebra i logika, Tome 47 (2008) no. 5, pp. 558-570.

Résumé

Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group $L$ of dimension $n$ over an arbitrary field of characteristic 2, we prove that any finite group $G$ isospectral to $L$ is isomorphic to an automorphic extension of $L$. An explicit formula is derived for the number of isomorphism classes of finite groups that are isospectral to $L$. This account is a continuation of the second author's previous paper where a similar result was established for finite simple linear groups $L$ in a sufficiently large dimension ($n>26$), and so here we confine ourselves to groups of dimension at most 26.

Détail

Keywords: finite simple group, linear group, order of element, spectrum of group, recognition by spectrum.

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