# On almost recognizability by spectrum of simple classical groups

Document Type: Research Paper

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Abstract

‎The set of element orders of a finite group $G$ is called the {\em spectrum}‎. ‎Groups with coinciding spectra are said to be {\em 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 $L\leq G\leq\Aut L$‎. ‎We show that the assertion remains true‎ ‎if 62 is replaced by 38‎.

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