Non-simple non-solvable finite groups whose maximal subgroups are all non-abelian simple or p-nilpotent (p odd) are p-nilpotent, resolving Kourovka Problems 19.57 and 19.58, with a complete p=2 classification.
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On two questions from the Kourovka Notebook concerning maximal subgroups
Non-simple non-solvable finite groups whose maximal subgroups are all non-abelian simple or p-nilpotent (p odd) are p-nilpotent, resolving Kourovka Problems 19.57 and 19.58, with a complete p=2 classification.