This article is cited in 2 papers

On periodic groups isospectral to $a_7$. ii

A. S. Mamontov^a, E. Jabara<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Dipartimento di Filosofia e Beni Culturali, Universitá di Ca'Foscari, Dorsoduro 3484/D-30123 Venezia, Italy

Abstract: Let $G$ be a periodic group and let $\omega(G)$ be the spectrum of $G$. We prove that if $G$ is isospectral to $A_7$, the alternating group of degree $7$ (i.e., $\omega(G)$ is equal to the spectrum of $A_7$); then $G$ has a finite nonabelian simple subgroup.

Keywords: periodic group, locally finite group, spectrum.

UDC: 517.518.85

Received: 07.05.2020
Revised: 04.06.2020
Accepted: 17.06.2020

DOI: 10.33048/smzh.2020.61.610

 English version: Siberian Mathematical Journal, 2020, 61:6, 1093–1101

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