The Root-Class Residuality of the Fundamental Groups of Certain Graphs of Groups with Central Edge Subgroups

Consider a class  of groups which contains at least one nontrivial group and is closed under subgroups, extensions, and direct products of the form , where and  is an isomorphic copy of  for each . Suppose that  is either a tree product of finitely many groups with central edge subgroups or the fund...

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Bibliographic Details
Published inSiberian mathematical journal Vol. 62; no. 6; pp. 1119 - 1132
Main Author Sokolov, E. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.11.2021
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Subgroups
512.543
root-class residuality of groups
HNN-extension
residual finiteness
residual solvability
tree product
fundamental groups of graphs of groups
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Summary:Consider a class  of groups which contains at least one nontrivial group and is closed under subgroups, extensions, and direct products of the form , where and  is an isomorphic copy of  for each . Suppose that  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  to be residually a  -group.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446621060136