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This article is cited in 12 scientific papers (total in 12 papers)
The root class residuality of the tree product of groups with amalgamated retracts
E. A. Tumanova Ivanovo State University, Ivanovo, Russia
Abstract:
Given a root class $\mathscr{K}$ of groups, we prove that the tree product of residually $\mathscr{K}$-groups with amalgamated retracts is a residually $\mathscr{K}$-group. This yields a criterion for the $\mathscr{K}$-residuality of Artin and Coxeter groups with tree structure. We also prove that the HNN-extension $X$ of a residually $\mathscr{K}$-group $B$ is a residually $\mathscr{K}$-group provided that the associated subgroups of $X$ are retracts in $B$ and $\mathscr{K}$ contains at least one nonperiodic group.
Keywords:
tree product of groups, HNN-extension, Artin group, Coxeter group, root class residuality, residual finiteness, residual $p$-finiteness, residual solubility.
Received: 08.10.2018 Revised: 14.01.2019 Accepted: 12.03.2019
Citation:
E. A. Tumanova, “The root class residuality of the tree product of groups with amalgamated retracts”, Sibirsk. Mat. Zh., 60:4 (2019), 891–906; Siberian Math. J., 60:4 (2019), 699–708
Linking options:
https://www.mathnet.ru/eng/smj3123 https://www.mathnet.ru/eng/smj/v60/i4/p891
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Abstract page: | 205 | Full-text PDF : | 212 | References: | 18 | First page: | 1 |
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