Geodesic
Residual properties of automorphisms groups and split extensions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2015), pp. 3-13.

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Let a group $G$ satisfy condition A: for every positive integer $n$ the number of all subgroups of the group $G$ of index $n$ is finite. We prove that if $G$ is virtually residually finite $p$-group for some prime $p$, then the automorphism group of the group $G$ is virtually residually finite $p$-group. A similar result is obtained for a split extension of the group $G$ by virtually residually finite $p$-group. Moreover, we prove that if the group $G$ is a virtually residually finite nilpotent $\pi$-group for some finite set $\pi$ of primes, then the automorphism group of the group $G$ and the split extension of the group $G$ by a virtually residually finite nilpotent $\pi$-group are virtually residually finite nilpotent $\pi$-groups.
Keywords: linear group, virtually residually finite $p$-group.
Mots-clés : automorphism group 
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     author = {D. N. Azarov},
     title = {Residual properties of automorphisms groups and split extensions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--13},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_8_a0/}
}
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D. N. Azarov. Residual properties of automorphisms groups and split extensions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2015), pp. 3-13. http://geodesic.mathdoc.fr/item/IVM_2015_8_a0/

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