This article is cited in 3 papers

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.

MSC: 20B27, 20E08, 20B22, 20B35, 20F65, 20B07

Received: 09.03.2015
Revised: 09.03.2015

Language: English

Bibliographic databases:

• 
•