The normal index of a maximal subgroup of a finite group-Reference-Cited by-同舟云学术

The normal index of a maximal subgroup of a finite group

Published:1989 Issue:1 Volume:106 Page:25-32
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Mukherjee N. P.,Bhattacharya Prabir

Abstract

For a maximal subgroup M M of a finite group G G , the normal index η ( G : M ) \eta (G:M) is defined to be the order of a chief factor H / K H/K where H H is minimal in the set of supplements of M M in G G . We obtain several results on the normal index of maximal subgroups M M of composite index in G G with [ G : M ] p = 1 {[G:M]_p} = 1 which imply G G to be solvable, supersolvable.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1989-106-01/S0002-9939-1989-0952319-9/S0002-9939-1989-0952319-9.pdf

Reference14 articles.

1. Classes of finite groups and their properties;Baer, Reinhold;Illinois J. Math.,1957

2. The normal index of maximal subgroups in finite groups;Beidleman, J. C.;Illinois J. Math.,1972

3. H. C. Bhatia, A generalized Frattini subgroup of a finite group. Ph.D. thesis, Michigan State Univ., East Lansing, 1972.

4. A family of maximal subgroups containing the Sylow subgroups and some solvability conditions;Bhattacharya, Prabir;Arch. Math. (Basel),1985

5. On the intersection of a class of maximal subgroups of a finite group. II;Bhattacharya, Prabir;J. Pure Appl. Algebra,1986

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. THE NORMAL INDEX OF SUBGROUPS IN FINITE GROUPS;Asian-European Journal of Mathematics;2010-09

2. On the normal indices of proper subgroups of finite groups;Journal of Pure and Applied Algebra;2010-07

3. On maximal subgroups of finite groups and theta pairs;Communications in Algebra;1996-01