A characterization property of the simple group \(\text{PSL}_4(5)\) by the set of its element orders. (English) Zbl 1156.20013

Summary: Let \(\omega(G)\) denote the set of element orders of a finite group \(G\). If \(H\) is a finite non-Abelian simple group and \(\omega(H)=\omega(G)\) implies \(G\) contains a unique non-Abelian composition factor isomorphic to \(H\), then \(G\) is called quasirecognizable by the set of its element orders. In this paper we prove that the group \(\text{PSL}_4(5)\) is quasirecognizable.


20D06 Simple groups: alternating groups and groups of Lie type
20D60 Arithmetic and combinatorial problems involving abstract finite groups
20G40 Linear algebraic groups over finite fields
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