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

 

The normal index of a maximal subgroup of a finite group


Authors: N. P. Mukherjee and Prabir Bhattacharya
Journal: Proc. Amer. Math. Soc. 106 (1989), 25-32
MSC: Primary 20E28; Secondary 20D10
MathSciNet review: 952319
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Abstract: For a maximal subgroup $ M$ of a finite group $ G$, the normal index $ \eta (G:M)$ is defined to be the order of a chief factor $ H/K$ where $ H$ is minimal in the set of supplements of $ M$ in $ G$. We obtain several results on the normal index of maximal subgroups $ M$ of composite index in $ G$ with $ {[G:M]_p} = 1$ which imply $ G$ to be solvable, supersolvable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0952319-9
PII: S 0002-9939(1989)0952319-9
Keywords: Solvable, supersolvable, $ p$-solvable
Article copyright: © Copyright 1989 American Mathematical Society