Leschenko Y. Sylow structure of the inductive limits of symmetric groups

Thesis is devoted to Sylow structure of the homogene-ous symmetric group Sp** of superdegree p**. We have distinguished two continuum classes of Sylow p-subgroups in Sp , each of which is split into continuum number of pairwise conjugated groups subclasses, and found the conjugation criterion in each of these classes. We have constructed the natural non residually finite Sylow p-subgroup of Sp**. In this subgroup we have distinguished the class of parallelotope subgroups. It is shown that if p>2 then the classes of normal parallelotope and characteristic subgroups of this group coincide. We have found the natural residually finite Sylow p-subgroup of Sp**. It is proved that if p > 2 then each fully invariant subgroup of this group is an entry of its lower central series.