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

Darafsheh, Mohammad Reza; Farjami, Yaghoub; Sadrudini, Abdollah

Arch. Math., Brno 43, No. 1, 31-37 (2007).

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.

MSC:

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

Keywords:

projective special linear groups; sets of element orders; quasirecognizable groups