Wenbin Guo, D. V. Lytkina, V. D. Mazurov, “Infinite groups containing a proper Hughes subgroup <nobr>$H_3(G)$</nobr>”, Algebra Logika, 2021, Volume 60, Number 3,Pages <nobr>298–302</nobr>

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Algebra Logika, 2021 Volume 60, Number 3, Pages 298–302 (Mi al2664)

Infinite groups containing a proper Hughes subgroup $H_3(G)$

Wenbin Guo^ab, D. V. Lytkina^cd, V. D. Mazurov^d

^a School Sci., Hainan Univ., Haikou, Hainan, P. R. CHINA
^b School Math. Sci., Univ. Sci. Tech. China, Hefei, P. R. CHINA
^c Siberian State University of Telecommunications and Informatics, Novosibirsk
^d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We consider groups in which $H_3(G)$ is both nontrivial and proper. In particular, it is proved that in such a group, $|G:H_3(G)|=3$.

Keywords: Hughes subgroup, Engel group, group of exponent $3$.

UDC: 512.542

Received: 02.07.2021
Revised: 18.10.2021

DOI: 10.33048/alglog.2021.60.303

English version: Algebra and Logic, 2021, 60:3, 196–199

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© Steklov Math. Inst. of RAS, 2025