On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank
https://doi.org/10.18255/1818-1015-2013-1-124-132
Abstract
Let G be a free product of residually finite virtually soluble groups A and B of finite rank with an amalgamated subgroup H, H 6= A and H 6= B. And let H contains a subgroup W of finite index which is normal in both A and B. We prove that the group G is residually finite if and only if the subgroup H is finitely separable in A and B. Also we prove that if all subgroups of A and B are finitely separable in A and B, respectively, all finitely generated subgroups of G are finitely separable in G.
About the Author
A. V. Rozov
Ivanovo State University
Russian Federation
Russian Federation
аспирант,
ul. Ermaka, 39, Ivanovo, 153025 Russia
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Review
For citations:
Rozov A.V. On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank. Modeling and Analysis of Information Systems. 2013;20(1):124-132. (In Russ.) https://doi.org/10.18255/1818-1015-2013-1-124-132
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