Invariant p-complements normalized by the fixed point subgroup

Let a group A act on a group G coprimely, i.e., $\left(\right|A|,|G\left|\right)=1$. We say that G is A-p-nilpotent if G has an A-invariant $\mathrm{Hall}{p}^{\prime }$-subgroup normalized by $C_G\left(A\right)$. In this paper, we give some equivalent descriptions on A-p-nilpotence by analyzing the structure of minimal non-A-p-nilpotent groups. This is a follow-up work to A. Beltrán's research.