A new characteristic subgroup for pushing up I

Abstract

Let T be a finite p-group. In this paper we introduce a new characteristic subgroup $W\left(T\right)$ of T containing $Z\left(T\right)$. This subgroup allows to give the structure of p-minimal finite groups G of characteristic p with ${\mathrm{PSL}}_2\left(p^n\right)$-factor group which satisfy $Z\left(T\right)⋬G$ and $W\left(T\right)⋬G$. This result generalizes a classical pushing up result obtained by Baumann [1] (for $p=2$) and Niles [8].