On finite groups isospectral to simple groups

A. Vasil'ev

The set of element orders of a finite group \(G\) is called the spectrum of \(G\). Finite groups are said to be isospectral if their spectra coincide. The topic we discuss is the structure of an arbitrary finite group \(G\) isospectral to a given finite simple group \(L\). Victor Mazurov conjectured that for most of non-abelian simple groups \(L\), the group \(G\) should be squeezed between \(L\) and its automorphism group, that is \(L\leqslant G\leqslant\operatorname{Aut}(L)\). We are going to show that, in a certain precise sense, this conjecture is true.

See also the author's pdf version: