Journal ArticleDOI
Approximability of HNN-extensions with central associated subgroups by a root class of groups
TLDR
In this article, the root property of a group with central associated subgroups is considered and several conditions are obtained for the approximability of such HNN-extensions by a class of groups which are closed with respect to factorization.Abstract:
HNN-extensions of a group with central associated subgroups are considered. Several conditions are obtained for the approximability of such HNN-extensions by a class of groups which have the root property and is closed with respect to factorization.read more
Citations
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Journal ArticleDOI
On the root-class residuality of generalized free products with a normal amalgamation
TL;DR: In this article, necessary and sufficient conditions for the free product of two groups with normal amalgamated subgroups to be a residually C-group were obtained, where C is a root class of groups which must be homomorphically closed in most cases.
Journal ArticleDOI
Sufficient conditions for the root-class residuality of certain generalized free products
E. V. Sokolov,E. A. Tumanova +1 more
TL;DR: In this article, the root-class residuality of a generalized free product of two residually K -groups with amalgamated subgroups with a retract of one of the factors is established.
Journal ArticleDOI
The Root Class Residuality of the Tree Product of Groups with Amalgamated Retracts
TL;DR: In this paper, it was shown that the tree product of groups with amalgamated retracts is a group with tree structure, which yields a criterion for the residualness of Artin and Coxeter groups with tree structures.
Journal ArticleDOI
Root class residuality of HNN-extensions with central cyclic associated subgroups
E. V. Sokolov,E. A. Tumanova +1 more
TL;DR: In this paper, a criterion for the R-residuality of an HNN-extension whose associated subgroups are cyclic and belong to the center of the base group is obtained.
Journal ArticleDOI
On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups
E. V. Sokolov,E. A. Tumanova +1 more
TL;DR: In this paper, the authors prove a criterion for G to be residually a ∆-k-group provided AutG(H) is an abelian group or satisfies some other conditions.
References
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Journal ArticleDOI
Subgroups of HNN Groups and Groups with one Defining Relation
A. Karrass,D. Solitar +1 more
TL;DR: In this article, the authors use the results in [6] to obtain a structure theorem for the subgroups of an HNN group and give several applications, e.g., the notion of a tree product as defined in [7] will also be needed.