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

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

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 roote...

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Bibliographic Details
Main Authors: Bier, Agnieszka, Sushchansky, Vitaliy
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Sylow \(p\)-subgroups of wreath products of groups
homogeneous rooted trees
automorphisms of trees
20B27
20E08
20B22
20B35
20F65
20B07
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1172
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Summary: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.

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