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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2015, Volume 19, Issue 1, Pages 19–38 (Mi adm503)

RESEARCH ARTICLE

Kaluzhnin's representations of Sylow $p$-subgroups of automorphism groups of $p$-adic rooted trees

Agnieszka Bier, Vitaliy Sushchansky

Silesian University of Technology, Institute of Mathematics

Abstract: The paper concerns the Sylow $p$-subgroups of automorphism groups of level homogeneous rooted trees. We recall and summarize the results obtained by L. Kaluzhnin on the structure of Sylow $p$-subgroups of isometry groups of ultrametric Cantor $p$-spaces in terms of automorphism groups of rooted trees. Most of the paper should be viewed as a systematic topical survey, however we include some new ideas in last sections.

Keywords: Sylow $p$-subgroups of wreath products of groups, homogeneous rooted trees, automorphisms of trees.

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Bibliographic databases:

MSC: 20B27, 20E08, 20B22, 20B35, 20F65, 20B07
Revised: 09.03.2015
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Citation: Agnieszka Bier, Vitaliy Sushchansky, “Kaluzhnin's representations of Sylow $p$-subgroups of automorphism groups of $p$-adic rooted trees”, Algebra Discrete Math., 19:1 (2015), 19–38

Citation in format AMSBIB
\Bibitem{BieSus15} \by Agnieszka~Bier, Vitaliy~Sushchansky \paper Kaluzhnin's representations of Sylow $p$-subgroups of automorphism groups of $p$-adic rooted trees \jour Algebra Discrete Math. \yr 2015 \vol 19 \issue 1 \pages 19--38 \mathnet{http://mi.mathnet.ru/adm503} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3376336} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000209846200003}