Maximal subgroups of prime index in a finite solvable group
HTML articles powered by AMS MathViewer
- by Paul Venzke PDF
- Proc. Amer. Math. Soc. 68 (1978), 140-142 Request permission
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.References
- Bertram Huppert, Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. 60 (1954), 409–434 (German). MR 64771, DOI 10.1007/BF01187387
- Otto H. Kegel, On Huppert’s characterization of finite supersoluble groups, Proc. Internat. Conf. Theory of Groups (Canberra, 1965) Gordon and Breach, New York, 1967, pp. 209–215. MR 0217183
- Paul Venzke, System quasinormalizers in finite solvable groups, J. Algebra 44 (1977), no. 1, 160–168. MR 437638, DOI 10.1016/0021-8693(77)90170-3
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 140-142
- MSC: Primary 20D10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0476851-2
- MathSciNet review: 0476851