Geodesic
On the virtual residuality a finite $p$-groups of descending HNN-extension
Čebyševskij sbornik, Tome 13 (2012) no. 1, pp. 9-19

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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. 
@article{CHEB_2012_13_1_a1,
     author = {D. N. Azarov},
     title = {On the virtual residuality a finite $p$-groups of descending {HNN-extension}},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {9--19},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2012_13_1_a1/}
}
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D. N. Azarov. On the virtual residuality a finite $p$-groups of descending HNN-extension. Čebyševskij sbornik, Tome 13 (2012) no. 1, pp. 9-19. http://geodesic.mathdoc.fr/item/CHEB_2012_13_1_a1/