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Sylow towers in groups where the index of every non-nilpotent maximal subgroup is prime
Preview AbstractIn this paper, we prove that if every non-nilpotent maximal subgroup of a finite group G has prime index then G has a Sylow tower.
Some generalizations of Shao and Beltrán’s theorem
Preview AbstractLet G and A be finite groups of relative coprime orders and A act on G via automorphisms. In this paper, we prove that when every maximal A-invariant subgroup of G that contains the normalizer of some Sylow subgroup has prime index, then G is supersolvable; if every non-nilpotent maximal A-invariant subgroup of G has prime index or is normal in G, then G is a Sylow tower group.