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Guo, W.; Lytkina, D. V.; Mazurov, V. D.

Infinite groups containing a proper Hughes subgroup \(H_3(G)\). (English. Russian original) Zbl 1515.20132

Algebra Logic 60, No. 3, 196-199 (2021); translation from Algebra Logika 60, No. 3, 298-302 (2021).
Summary: We consider groups in which \(H_3(G)\) is both nontrivial and proper. In particular, it is proved that in such a group, \(|G : H_3(G)| = 3\).

MSC:

20E07 Subgroup theorems; subgroup growth
20E34 General structure theorems for groups

Keywords:

Hughes subgroup; Engel group; group of exponent 3
PDFBibTeX XMLCite
\textit{W. Guo} et al., Algebra Logic 60, No. 3, 196--199 (2021; Zbl 1515.20132); translation from Algebra Logika 60, No. 3, 298--302 (2021)
Full Text: DOI

References:

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