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

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.