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On a Family of Residually Finite Groups
D. I. Moldavanskii Ivanovo State University
Abstract:
As is known, there is a finitely generated residually finite group (for short, a residually $\mathcal F$-group) whose extension by some finite group is not a residually $\mathcal F$-group. In the paper, it is shown that, nevertheless, every extension of a finite group by a finitely generated residually $\mathcal F$-group is a Hopf group, and every extension of a center-free finite group by a finitely generated residually $\mathcal F$-group is a residually $\mathcal F$-group. If a finitely generated residually $\mathcal F$-group $G$ is such that every extension of an arbitrary finite group by $G$ is a residually $\mathcal F$-group, then a descending HNN-extension of the group $G$ also has the same property, provided that it is a residually $\mathcal F$-group.
Keywords:
residually finite groups, HNN-extensions of groups.
Received: 20.06.2017
Citation:
D. I. Moldavanskii, “On a Family of Residually Finite Groups”, Mat. Zametki, 105:1 (2019), 65–75; Math. Notes, 105:1 (2019), 56–63
Linking options:
https://www.mathnet.ru/eng/mzm11726https://doi.org/10.4213/mzm11726 https://www.mathnet.ru/eng/mzm/v105/i1/p65
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Abstract page: | 293 | Full-text PDF : | 33 | References: | 25 | First page: | 15 |
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