The influence of second maximal subgroups on the generalized p-solvability of finite groups

On some second maximal subgroups of non-solvable groups

“…(3) A has the cover and avoidance properties in G, in brevity, A is a CAP -subgroup of G, if A either covers or avoids every chief factor of G. Lemma 2.5. [16,Lemma 2.13] Let H be a second maximal subgroup of a group G and Theorem 2] Let G be a finite group such that, for all primes p, N G (P ) is nilpotent where P is a Sylow p-subgroup of G. Then G is nilpotent. Lemma 2.9.…”