This article is cited in 1 paper

Unsolvability of finite groups isospectral to the automorphism group of the second sporadic Janko group

A. Kh. Zhurtov^a, D. V. Lytkina^bc, V. D. Mazurov<sup>bd

a</sup> Kabardino-Balkar State University, Nal'chik
^b Siberian State University of Telecommunications and Informatics, Novosibirsk
^c Novosibirsk State University
^d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: For a finite group $G$, the spectrum is the set $\omega(G)$ of element orders of the group $G$. The spectrum of $G$ is closed under divisibility and is therefore uniquely determined by the set $\mu(G)$ consisting of elements of $\omega(G)$ that are maximal with respect to divisibility. We prove that a finite group isospectral to ${\rm Aut}(J_2)$ is unsolvable.

Keywords: spectrum, automorphism group, Janko group.

UDC: 512.542

Received: 25.07.2023
Revised: 30.10.2023

DOI: 10.33048/alglog.2023.62.104

 English version: Algebra and Logic, 2023, 62:1, 50–53