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Mathematical Notes

, Volume 105, Issue 1–2, pp 56–63 | Cite as

On a Family of Residually Finite Groups

  • D. I. MoldavanskiiEmail author
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Abstract

It is known that there exists a finitely generated residually finite group (for short, a residually F-group) the extension by which of some finite group is not a residually F-group. In the paper, it is shown that, nevertheless, every extension of a finite group by a finitely generated residually F-group is a Hopf group, and every extension of a center-free finite group by a finitely generated residually F-group is a residually F-group. If a finitely generated residually F-group G is such that every extension of an arbitrary finite group by G is a residually F-group, then a descending HNN-extension of the group G also has the same property, provided that it is a residually F-group.

Keywords

residually finite groups HNN-extensions of groups 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Ivanovo State UniversityIvanovoRussia

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