Normality conditions in the Sylow $\mathbf{p}$-subgroup of $\mathrm{Sym}({\mathbf{p}}^{\mathbf{n}})$ and its associated Lie algebra

Riccardo Aragona, Norberto Gavioli, Giuseppe Nozzi

In this work, we give a description of the structure of the normal subgroups of a Sylow $p$-subgroup $W_n$ of $\mathrm{Sym}(p^n)$, showing that they contain a term from the lower c…