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This article is cited in 5 scientific papers (total in 5 papers)
On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups
E. V. Sokolov Ivanovo State University
Abstract:
Let $\mathcal{C}$ be an arbitrary class of groups which has the root property, consists of finite groups only, and contains at least one nonidentity group. It is proved that every extension of a free group by a $\mathcal{C}$-group is conjugacy $\mathcal{C}$-separable. It is also proved that, if $G$ is a free product of two conjugacy $\mathcal{C}$-separable groups with finite amalgamated subgroup or an HNN-extension of a conjugacy $\mathcal{C}$-separable group with finite associated subgroups, then the group $G$ is residually $\mathcal{C}$ if and only if it is conjugacy $\mathcal{C}$-separable.
Keywords:
class of groups which has the root property, HNN-extension, free product with finite amalgamated subgroup, residually $\mathcal{C}$ group, conjugacy $\mathcal{C}$-separable group.
Received: 22.09.2013
Citation:
E. V. Sokolov, “On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups”, Mat. Zametki, 97:5 (2015), 767–780; Math. Notes, 97:5 (2015), 779–790
Linking options:
https://www.mathnet.ru/eng/mzm10396https://doi.org/10.4213/mzm10396 https://www.mathnet.ru/eng/mzm/v97/i5/p767
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Abstract page: | 260 | Full-text PDF : | 114 | References: | 33 | First page: | 11 |
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