On 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 the paper we determine all finite groups isospectral to the simple groups $S_6(q)$, $O_7(q)$, and $O_8^{+}(q)$. In particular, we prove that with just four exceptions, every such a finite group is an extension of the initial simple group by a (possibly trivial) field automorphism.

References in corpus (1)

• On finite groups isospectral to simple classical groups

Cited by in corpus (3)

• Criterion of unrecognizability of a finite group by its Gruenberg-Kegel graph
• Finite groups isospectral to simple groups
• On the nilpotency of the solvable radical of a finite group isospectral to a simple group