1978•Proceedings of the American Mathematical SocietyRequires access
Maximal subgroups of prime index in a finite solvable group
Paul Venzke
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Abstract
In this note we show that a maximal subgroup of a finite solvable group has prime index if and only if it admits a cyclic supplement which permutes with one of its Sylow systems. In particular, a finite solvable group is supersolvable if and only if each maximal subgroup admits a cyclic supplement which permutes with a Sylow system of the maximal subgroup.