Geodesic
On the virtually residually $p$-finiteness of free product of polycyclic groups with normal amalgamated subgroups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 64-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a free product of polycyclic groups $A$ and $B$ with normal amalgamated subgroups $H$ and $K$. We prove that, for any prime $p$, the group $G$ is a virtually residually finite $p$-group.
Keywords: generalized free product, virtually residually a finite $p$-group.
Mots-clés : polycyclic group 
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     title = {On the virtually residually $p$-finiteness of free product of polycyclic groups with normal amalgamated subgroups},
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A. V. Rozov. On the virtually residually $p$-finiteness of free product of polycyclic groups with normal amalgamated subgroups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 64-71. http://geodesic.mathdoc.fr/item/IVM_2014_11_a6/

[1] Shmelkin A. L., “Politsiklicheskie gruppy”, Sib. matem. zhurn., 9:1 (1968), 234–235 | Zbl

[2] Gruenberg K. W., “Residual properties of infinite soluble groups”, Proc. London Math. Soc., 7:1 (1957), 29–62 | DOI | MR | Zbl

[3] Azarov D. N., Goltsov D. V., “Pochti approksimiruemost konechnymi $p$-gruppami svobodnogo proizvedeniya dvukh grupp s konechnymi ob'edinennymi podgruppami”, Vestn. Ivan. gos. un-ta, 2011, no. 2, 94–97

[4] Baumslag G., “On the residual finiteness of generalised free products of nilpotent groups”, Trans. Amer. Math. Soc., 106:2 (1963), 193–209 | DOI | MR | Zbl

[5] Azarov D. N., “O pochti approksimiruemosti konechnymi $p$-gruppami”, Chebyshevskii sbornik, 11:3 (2010), 11–21 | Zbl

[6] Rozov A. V., “Nekotorye approksimatsionnye svoistva svobodnykh proizvedenii razreshimykh grupp konechnogo ranga s normalnymi ob'edinennymi podgruppami”, Chebyshevskii sbornik, 13:1 (2012), 130–142 | MR | Zbl

[7] Plotkin B. I., Gruppy avtomorfizmov algebraicheskikh sistem, Nauka, M., 1966 | MR | Zbl

[8] Lindon R., Shupp P., Kombinatornaya teoriya grupp, Mir, M., 1980 | MR