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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 88–94 (Mi smj2842)  

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

W. Guoa, A. S. Mamontovbc

a 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.

Funding Agency Grant Number
National Natural Science Foundation of China 11371335
Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences
The first author was supported by the NNSF of China (11371335) and the Wu Wen-Tsuu Key Laboratory of Mathematics of the Chinese Academy of Science.


DOI: https://doi.org/10.17377/smzh.2017.58.109

Full text: PDF file (286 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:1, 67–71

Bibliographic databases:

UDC: 512.54
MSC: 35R30
Received: 04.12.2015

Citation: W. Guo, A. S. Mamontov, “On groups whose element orders divide $6$ and $7$”, Sibirsk. Mat. Zh., 58:1 (2017), 88–94; Siberian Math. J., 58:1 (2017), 67–71

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