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Chebyshevskii Sb., 2012, Volume 13, Issue 1, Pages 9–19 (Mi cheb10)  

This article is cited in 6 scientific papers (total in 6 papers)

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.

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UDC: 512.543
Received: 14.05.2012

Citation: D. N. Azarov, “On the virtual residuality a finite $p$-groups of descending HNN-extension”, Chebyshevskii Sb., 13:1 (2012), 9–19

Citation in format AMSBIB
\Bibitem{Aza12}
\by D.~N.~Azarov
\paper On the virtual residuality a finite $p$-groups of descending HNN-extension
\jour Chebyshevskii Sb.
\yr 2012
\vol 13
\issue 1
\pages 9--19
\mathnet{http://mi.mathnet.ru/cheb10}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. N. Azarov, “On the residual finiteness of the HNN-extensions and generalized free products of finite rank groups”, Siberian Math. J., 54:6 (2013), 959–967  mathnet  crossref  mathscinet  isi
    2. D. N. Azarov, “Approximability of soluble groups of finite rank by certain classes of finite groups”, Russian Math. (Iz. VUZ), 58:8 (2014), 15–23  mathnet  crossref
    3. E. A. Tumanova, “Ob approksimiruemosti kornevymi klassami HNN-rasshirenii grupp”, Model. i analiz inform. sistem, 21:4 (2014), 148–180  mathnet
    4. D. I. Moldavanskii, “Kombinatornaya teoriya grupp v Ivanovskom gosudarstvennom universitete”, Chebyshevskii sb., 15:4 (2014), 32–54  mathnet
    5. D. V. Goltsov, “Approksimiruemost fundamentalnoi gruppy konechnogo grafa grupp kornevym klassom grupp”, Chebyshevskii sb., 17:3 (2016), 64–71  mathnet  elib
    6. D. N. Azarov, “O finitno approksimiruemykh gruppakh konechnogo obschego ranga”, Matem. zametki, 101:3 (2017), 323–329  mathnet  crossref  mathscinet  elib
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