The Root-Class Residuality of Tree Products with Central Amalgamated Subgroups

Given a root class C of groups and a tree product P in which each amalgamated subgroup lies in the centers of the corresponding vertex groups, we point out certain sufficient conditions for the C -residuality of P . In particular, we show that the tree product of solvable groups of bounded derived l...

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Bibliographic Details
Published inSiberian mathematical journal Vol. 61; no. 3; pp. 545 - 551
Main Authors Sokolov, E. V., Tumanova, E. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2020
Springer Nature B.V
Subjects
Amalgamation
Mathematics
Mathematics and Statistics
Subgroups
residual finiteness
root-class residuality
residual
residual solvability
tree product
finiteness
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Summary:Given a root class C of groups and a tree product P in which each amalgamated subgroup lies in the centers of the corresponding vertex groups, we point out certain sufficient conditions for the C -residuality of P . In particular, we show that the tree product of solvable groups of bounded derived length with central amalgamated subgroups is residually solvable.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446620030180