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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximal subgroups of prime index in a finite solvable group


Author: Paul Venzke
Journal: Proc. Amer. Math. Soc. 68 (1978), 140-142
MSC: Primary 20D10
MathSciNet review: 0476851
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0476851-2
PII: S 0002-9939(1978)0476851-2
Keywords: Maximal subgroup, supersolvable, quasinormal
Article copyright: © Copyright 1978 American Mathematical Society