On root-class residuality of generalized free products

Details On root-class residuality of generalized free products On root-class residuality of generalized free products

2004-08-20

arxiv.org/abs/math/0408277v1

Nauch. Trudy IvGU, vol. 5, 2002, p.6-10 (in Russian)

Mathematics

Group Theory

6 pages

Scientific paper

Root-class residuality of free product of root-class residual groups is demonstrated. A sufficient condition for root-class residuality of generalized free product $G$ of groups $A$ and $B$ amalgamating subgroups $H$ and $K$ through the isomorphism $\phi$ is derived. For the particular case when $A=B$, $H=K$ and $\phi$ is the identity mapping, it is shown that group $G$ is root-class residual if and only if $A$ is root-class residual and subgroup $H$ of $A$ is root-class closed. These results are extended to generalized free product of infinitely many groups amalgamating a common subgroup.

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