Minimal generating sets and Cayley graphs of Sylow p-subgroups of finite symmetric groups

Abstract

Minimal generating sets of a Sylow p-subgroup Pn of the symmetric group Spn are characterized. The number of ordered minimal generating sets of Pn is calculated. The notion of the type of a generating set of Pn is introduced and it is proved that Pn contains minimal generating sets of all possible type. The isomorphism problem of Cayley graphs of Pn with respect to their minimal generating sets is discussed.