A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group

A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group

Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable,...

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Main Authors: Na Tang, Xianhua Li
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/921804
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spelling doaj-60a09888ac4f45f5ab8723afa81a4af22020-11-24T23:56:18ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/921804921804A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite GroupNa Tang0Xianhua Li1School of Mathematical Science, Soochow University, Suzhou 215006, ChinaSchool of Mathematical Science, Soochow University, Suzhou 215006, ChinaLet M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable, and p-nilpotent.http://dx.doi.org/10.1155/2014/921804
collection DOAJ
language English
format Article
sources DOAJ
author Na Tang
Xianhua Li
spellingShingle Na Tang
Xianhua Li
A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
Journal of Applied Mathematics
author_facet Na Tang
Xianhua Li
author_sort Na Tang
title A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
title_short A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
title_full A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
title_fullStr A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
title_full_unstemmed A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group
title_sort note on the normal index and the c-section of maximal subgroups of a finite group
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. Using the concepts of normal index and c-section, we obtain some new characterizations of p-solvable, 2-supersolvable, and p-nilpotent.
url http://dx.doi.org/10.1155/2014/921804
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AT natang noteonthenormalindexandthecsectionofmaximalsubgroupsofafinitegroup
AT xianhuali noteonthenormalindexandthecsectionofmaximalsubgroupsofafinitegroup
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