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关于极大子群指数的一个注记
  • ISSN号：1004-8820
  • 期刊名称：烟台大学学报(自然科学与工程版)
  • 时间：2015.1
  • 页码：1-2
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：烟台大学数学与信息科学学院
  • 相关基金：国家自然科学基金资助项目(11201401,11201403,11361075)
  • 相关项目：点传递图中若干问题的研究
作者： 史江涛|张翠|
关键词： 有限群, 单群, 极大子群指数, 可解性, Sylow子群
中文摘要：

《Journal of Algebra》第321卷第5期的论文《A note on p-nilpotence and solvability of finite groups》中的定理13讨论了某些极大子群指数为素数的有限群的可解性,本文给出了该定理一个新的证明,并进一步证明了:如果有限群G满足对于每个Sylow子群P均有或者P正规于G或者G的包含NG(P)的极大子群有素数指数,那么G一定是可解的.

英文摘要：

Theorem 13 of 《A note on p-nilpotence and solvability of finite groups, Journal of Algebra, 321 (5)》asserts the solvability of finite groups in which some maximal subgroups have prime indices. In this paper, we offer a new proof for this theorem. Further, we show that if G is such a finite group that either its each Sylow subgroup P is normal in G or the maximal subgroup of G containing NG ( P) has prime index, then G must be solvable.

同期刊论文项目
Frobenius定理的应用与子群的自同构导子
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点传递图中若干问题的研究
期刊论文 16
有限群的Frobenius谱集合与子群的共轭类型
期刊论文 48
同项目期刊论文
非平凡循环子群共轭类类数较小的有限非可解群
关于极大子群指数的一个注记Ⅱ
On an inverse problem to Frobenius' theorem II
On conjugacy class sizes of primary and biprimary elements of a finite group
Characterization of finitegroups by the number of non-cyclic non-TI-subgroups
Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements
p-divisibility of conjugacy class sizes and normal p-complements
Finite groups in which some particular subgroups are TI-subgroups
A note on TI-subgroups of a finite group
Finite groups in which all nonabelian subgroups are TI-subgroups
Finite groups having at most 27 non-normal proper subgroups of non-prime-power order
Finite groups with given quantitative non-nilpotent subgroups II
A note on the normalizer of Sylow 2-subgroup of special linear group SL_2(p^f)
Finite groups in which the centralizer of every minimal subgroup is cyclic
Finite groups with three conjugacy class sizes of certain elements
Corrigendum on the solvability of groups with four class sizes
On the orders of zeros of monolithic characters
Recognition of L2(q) by its group order and largest irreducible character degree
A new characterization of PSL2(p) by NSE
A classification of minimal non-MNP-groups
Conjugacy class sizes and solvability of finite groups
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Finite groups with some nonnormal subgroups of non-prime-power order
The influence of the number of non-(sub)normal non-abelian subgroups on solvability of finite groups
Finite non-solvable groups whose monolithic characters vanish on at most three conjugacy classes
On zero patterns of characters of finite groups
Class sizes of prime-power order p’-elements and normal subgroups
An extension of a theorem of Alan Camina's on conjugacy class sizes
Solvability of finite groups with four class sizes of certain elements
A note on the number of zeros in the columns of the character table of a group
The influence of the number of non-(sub)normalnon-abelian subgroups on solvability of finite groups
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A new characterization of some linear groups by nse
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非平凡循环子群共轭类类数较小的有限非可解群
Finite groups with few vanishing elements
Finite groups with some non-cyclic subgroups having small indices in their normalizers
非幂零极大子群共轭类类数给定的有限群
On the set of the numbers of conjugates of noncyclic proper subgroups of finite groups
A note on 2-nilpotence of finite groups
关于极大子群指数的一个注记Ⅱ
具有给定共轭类长的有限群（Ⅱ）
Finite groups with some subgroups of given order
Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup
Characterization of finite groups by the number of non-cyclic non-TI-subgroups
The influence of the number of non-(sub)normal non-abelian subgroups on solvability of finite groups
On non-normal non-abelian subgroups of finite groups
A note on finite groups with the indice of some maximal subgroups being primes
A remark on “A note on TI-subgroups of finite groups”
非平凡循环子群共轭类类数较小的有限非可解群
非幂零极大子群共轭类类数给定的有限群
Finite groups with non-cyclic 2-subgroups which are subnormal or have small indices in their normali
On a finite group in which every non-abelian subgroup is a TI-subgroup
关于极大子群指数的一个注记Ⅱ
期刊信息
  • 《烟台大学学报：自然科学与工程版》
  • 中国科技核心期刊
  • 主管单位:山东省教育厅
  • 主办单位:烟台大学
  • 主编：郭善利
  • 地址：山东省烟台市莱山区清泉路30号
  • 邮编：264005
  • 邮箱：xuebao@ytu.edu.cn
  • 电话：0535-6904913
  • 国际标准刊号：ISSN：1004-8820
  • 国内统一刊号：ISSN：37-1213/N
  • 邮发代号:
  • 获奖情况:
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  • 被引量:2538