Finite Groups with Given Quantitative Non-Nilpotent Subgroups II

Jiangtao Shi; Cui Zhang

doi:10.1080/00927872.2013.806523

Finite Groups with Given Quantitative Non-Nilpotent Subgroups II

Jiangtao Shi, Cui Zhang

Department of Applied Mathematics and Computer Science

Yantai University

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

As an extension of Shi and Zhang's 2011 article [4], we prove that any finite group having at most 23 non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5), and any finite group having at most three conjugacy classes of non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5).

Original language	English
Journal	Communications in Algebra
Volume	42
Issue number	10
Pages (from-to)	4248-4252
ISSN	0092-7872
DOIs	https://doi.org/10.1080/00927872.2013.806523
Publication status	Published - 2014

Keywords

Conjugacy classes
Non-normal
Non-nilpotent subgroup
Solvable group

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10.1080/00927872.2013.806523

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title = "Finite Groups with Given Quantitative Non-Nilpotent Subgroups II",

abstract = "As an extension of Shi and Zhang's 2011 article [4], we prove that any finite group having at most 23 non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5), and any finite group having at most three conjugacy classes of non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5).",

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AB - As an extension of Shi and Zhang's 2011 article [4], we prove that any finite group having at most 23 non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5), and any finite group having at most three conjugacy classes of non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5).

KW - Conjugacy classes

KW - Non-normal

KW - Non-nilpotent subgroup

KW - Solvable group

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DO - 10.1080/00927872.2013.806523

M3 - Journal article

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VL - 42

SP - 4248

EP - 4252

JO - Communications in Algebra

JF - Communications in Algebra

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Finite Groups with Given Quantitative Non-Nilpotent Subgroups II

Abstract

Keywords

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