Abstract
We prove that a finite group whose every maximal subgroup is simple or nilpotent is a Schmidt group. A group whose every maximal subgroup is simple or supersoluble can be nonsoluble, and in this case we prove that its chief series has the form 1 ⊂ K ⊆ G, K }~ PSL2(p) for a suitable prime p, |G: K| ≤ 2.
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