On groups whose element orders divide $6$ and $7$

W. Guo^a, A. S. Mamontov<sup>bc

a</sup> University of Science and Technology of China, School of Mathematical Science, Hefei, P. R. China
^b Sobolev Institute of Mathematics, Novosibirsk, Russia
^c Novosibirsk State University, Novosibirsk, Russia

Abstract: We prove that a group whose element orders divide $6$ and $7$ either is locally finite or an extension of a nontrivial elementary abelian $2$-group by a group without involutions.

Keywords: periodic group, locally finite group, spectrum.

UDC: 512.54

MSC: 35R30

Received: 04.12.2015

DOI: 10.17377/smzh.2017.58.109

 English version: Siberian Mathematical Journal, 2017, 58:1, 67–71

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