Geodesic
Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
Algebra and discrete mathematics, no. 4 (2009), pp. 167-184

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Minimal generating sets of a Sylow $p$-subgroup $P_n$ of the symmetric group $S_{p^n}$ are characterized. The number of ordered minimal generating sets of $P_n$ is calculated. The notion of the type of a generating set of $P_n$ is introduced and it is proved that $P_n$ contains minimal generating sets of all possible type. The isomorphism problem of Cayley graphs of $P_n$ with respect to their minimal generating sets is discussed.
Keywords: Cayley graph, Sylow $p$-subgroup, Frattini subgroup. 
@article{ADM_2009_4_a12,
     author = {Anna J. Slupik and Vitaly I. Sushchansky},
     title = {Minimal generating sets and {Cayley} graphs of {Sylow} $p$-subgroups of finite symmetric groups},
     journal = {Algebra and discrete mathematics},
     pages = {167--184},
     publisher = {mathdoc},
     number = {4},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2009_4_a12/}
}
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Anna J. Slupik; Vitaly I. Sushchansky. Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups. Algebra and discrete mathematics, no. 4 (2009), pp. 167-184. http://geodesic.mathdoc.fr/item/ADM_2009_4_a12/