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This article is cited in 5 scientific papers (total in 5 papers)
The root-class residuality of the fundamental groups of certain graphs of groups with central edge subgroups
E. V. Sokolov Ivanovo State University, Ivanovo, Russia
Abstract:
Consider a class $\mathcal{C}$ of groups which contains at least one nontrivial group and is closed under subgroups, extensions, and direct products of the form $\prod\nolimits_{y \in Y} X_{y}$, where $X, Y \in \mathcal{C}$ and $X_{y}$ is an isomorphic copy of $X$ for each $y \in Y$. Suppose that $G$ is either a tree product of finitely many groups with central edge subgroups or the fundamental group of an arbitrary graph of groups with trivially intersecting central edge subgroups. We establish some sufficient conditions for $G$ to be residually a $\mathcal{C}$-group.
Keywords:
root-class residuality of groups, residual finiteness, residual solvability, fundamental groups of graphs of groups, tree product, HNN-extension.
Received: 27.02.2021
Citation:
E. V. Sokolov, “The root-class residuality of the fundamental groups of certain graphs of groups with central edge subgroups”, Sibirsk. Mat. Zh., 62:6 (2021), 1382–1400; Siberian Math. J., 62:6 (2021), 1119–1132
Linking options:
https://www.mathnet.ru/eng/smj7635 https://www.mathnet.ru/eng/smj/v62/i6/p1382
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Abstract page: | 155 | Full-text PDF : | 22 | References: | 38 | First page: | 4 |
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