Recognition of symplectic and orthogonal groups of small dimensions by spectrum

Abstract

We refer to the set of the orders of elements of a finite group as its spectrum and say that finite groups are isospectral if their spectra coincide. In this paper, we determine all finite groups isospectral to the simple groups [Formula: see text], [Formula: see text], and [Formula: see text]. In particular, we prove that with just four exceptions, every such finite group is an extension of the initial simple group by a (possibly trivial) field automorphism.