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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 3, Pages 59–76 (Mi izv22)  

This article is cited in 7 scientific papers (total in 7 papers)

Normal subgroups of free constructions of profinite groups and the congruence kernel in the case of positive characteristic

P. A. Zalesskii

Institute of Technical Cybernetics, National Academy of Sciences of Belarus

Abstract: We prove the analogue of the Kurosh subgroup theorem for closed normal subgroups of free constructions of profinite groups and also corresponding analogues of abstract structural results for closed normal subgroups of more general free constructions of profinite groups (amalgamated free products, HNN-extensions). The structure theorem is used to obtain a description of the congruence-kernel $C$ of the arithmetic lattice $\Gamma$ of the group of $K$-rational points $G=\mathbf G(K)$ of a semisimple connected algebraic group $\mathbf G$ of $K$-rank 1 over a non-Archimedean local field $K$.

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English version:
Izvestiya: Mathematics, 1995, 59:3, 499–516

Bibliographic databases:

MSC: 20E18
Received: 15.04.1994

Citation: P. A. Zalesskii, “Normal subgroups of free constructions of profinite groups and the congruence kernel in the case of positive characteristic”, Izv. RAN. Ser. Mat., 59:3 (1995), 59–76; Izv. Math., 59:3 (1995), 499–516

Citation in format AMSBIB
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\by P.~A.~Zalesskii
\paper Normal subgroups of free constructions of profinite groups and the congruence kernel in the case of positive characteristic
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 3
\pages 59--76
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\zmath{https://zbmath.org/?q=an:0896.20023}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 3
\pages 499--516
\crossref{https://doi.org/10.1070/IM1995v059n03ABEH000022}
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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. Herfort W. Zalesskii P., “Cyclic Extensions of Free Pro-P Groups”, J. Algebra, 216:2 (1999), 511–547  crossref  mathscinet  zmath  isi
    2. Baumgartner U., “Cusps of Lattices in Rank 1 Lie Groups Over Local Fields”, Geod. Dedic., 99:1 (2003), 17–46  crossref  mathscinet  zmath  isi
    3. Mason A.W., Premet A., Sury B., Zalesskii P.A., “The Congruence Kernel of an Arithmetic Lattice in a Rank One Algebraic Group Over a Local Field”, J. Reine Angew. Math., 623 (2008), 43–72  crossref  mathscinet  zmath  isi
    4. Herfort W., Zalesskii P.A., “A Virtually Free Pro-P Need Not Be the Fundamental Group of a Profinite Graph of Finite Groups”, Arch. Math., 94:1 (2010), 35–41  crossref  mathscinet  zmath  isi
    5. Kochloukova D.H., Zalesskii P.A., “On Pro-P Analogues of Limit Groups via Extensions of Centralizers”, Math. Z., 267:1-2 (2011), 109–128  crossref  mathscinet  zmath  isi
    6. Kochloukova D.H., Zalesskii P.A., “Subdirect products of pro-p groups”, Math. Proc. Camb. Philos. Soc., 158:2 (2015), 289–303  crossref  mathscinet  isi  scopus
    7. Proc. Steklov Inst. Math., 292 (2016), 216–246  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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