Kaluzhnin's representations of Sylow \(p\)-subgroups of automorphism groups of \(p\)-adic rooted trees

Agnieszka Bier, Vitaliy Sushchansky

Abstract


The paper concerns theĀ  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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