On the influence of the fixed points of an automorphism to the structure of a group

Invariant complements normalized by the fixed point subgroup

“…We also want to note that a complete although weaker extension of the p-nilpotency theorem of Frobenius has appeared in [10]. It concerns, however, with the existence of normal p-complement instead of p-complement normalized by C. Theorem B of [10] establishes that, in the coprime action context, a group G is p-nilpotent when N G (P ) is p-nilpotent for every non-trivial invariant p-subgroup P of G.…”