In this article, we investigate generators and relations of syllows subgroups of some symmetric group. It will enable studying syllows subgroups of other groups since every finite subgroup is isomorphicaly embedded in the syllows subgroup of some symmetric group. We find a set of relations for a fixed system of generators and prove that this set of relations is minimal between sets of relations. Research methods are the method of Shreier"s canonical words and rewriting process. In addition, we prove that such subgroups have a finite presentation, notably it has finite number of generators and relation. We prove the existence of close connection of such subgroups with the iterated wreath product of cyclic subgroups with prime order - Cp. Therefore, it became the research subject. Also, we investigate the iterated wreath product, related to automaton group and transformations. Furthermore, the structure properties of symmetryc group pk S were previously studied, while we describe all other properties left. Specifically, we study commutants and corresponding verbal subgroups. We find the presentation for syllows p-subgroups of pk S and Sn.
З 31.12.2014 по 01.03.2015 Наукова бібліотека читачів не обслуговує.
