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 key L. Kaluzlmin on the structure of Sylow p-subgroups of isometry groups of tiltrametric Cantor p-spaces in terms of automorphism groups of rooted trees. iVlost of the paper should be viewed as a systematic topical survey, however we include some new ideas in last sections.