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On the virtual residuality a finite $p$-groups of descending HNN-extension

D. N. Azarov

Ivanovo State University

Abstract: Let $G$ be a group of finite general rank. And let $H$ be a finite index subgroup in $G$. Let $G(\varphi)$ be a descending HNN-extension, corresponding to isomorphism $\varphi : G \rightarrow H $. It is proved that if $G$ is virtually residually a finite $p$-group for any prime $p > [G:H]$, then $G(\varphi)$ is virtually residually a finite $p$-group. As a corollary a new proof of the known theorems is obtained.

UDC: 512.543

Received: 14.05.2012