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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
  • ISSN号：1001-6600
  • 期刊名称：广西师范大学学报(自然科学版)
  • 时间：2014
  • 页码：52-56
  • 分类：O152.1[理学—数学;理学—基础数学]
  • 作者机构：[1]烟台大学数学与信息科学学院,山东烟台264005
  • 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, 循环子群, 非可解群, finite group, cyclic subgroup, non-solvable group
中文摘要：

本文完全刻画非平凡循环子群共轭类类数不大于2的有限群的结构,证明了非平凡循环子群共轭类类数不大于4的有限非可解群仅有PSL2（r）,其中r=5,7,8,9。

英文摘要：

The structures of finite groups having at most two conjugacy classes of non-trivial cyclic subgroups are completely characterized.It is proven that a finite non-solvable group Ghaving at most four conjugacy classes of non-trivial cyclic subgroups must be isomorphic to PSL2（r）,where r=5,7,8,9.

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Frobenius定理的应用与子群的自同构导子
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同项目期刊论文
关于极大子群指数的一个注记
关于极大子群指数的一个注记Ⅱ
On an inverse problem to Frobenius' theorem II
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
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
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关于极大子群指数的一个注记
On a generalization of a theorem of Burnside
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
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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
Finite groups with three conjugacy class sizes of primary and biprimary elements
A new characterization of some linear groups by nse
A new characterization of Mathieu groups
Finite groups with few vanishing elements
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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
关于极大子群指数的一个注记
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
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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
Solvability of finite groups with four class sizes of certain elements
An extension of a theorem of Alan Camina's on conjugacy class sizes
A note on the normalizer of Sylow 2-subgroup of special linear group SL_2(p^f)
On conjugacy class sizes of primary and biprimary elements of a finite group
期刊信息
  • 《广西师范大学学报：自然科学版》
  • 北大核心期刊（2011版）
  • 主管单位:广西师范大学
  • 主办单位:广西师范大学
  • 主编：苏桂发
  • 地址：桂林市三里店育才路15号
  • 邮编：541004
  • 邮箱：gxsdzkb@mailbox.gxnu.edu.cn
  • 电话：0773-5848958
  • 国际标准刊号：ISSN：1001-6600
  • 国内统一刊号：ISSN：45-1067/N
  • 邮发代号:48-54
  • 获奖情况:
  • 1994年，获广西优秀期刊三等奖,1995年，获广西高校理科学报B类一等奖,1996年，获广西第三届优秀报刊二等奖,1999年，获广西首届高校优秀学报二等奖,2001年，被评为第四届广西优秀科技期刊,2002年，获第二届广西高校优秀学报二等奖,2002年，入选中国期刊方阵“双效”期刊,2004年，获全国高校优秀科技期刊一等奖,2005年，获第五届“广西十佳自然科学期刊”称号,2007年，获第六届“广西十佳自然科学期刊”称号,2008年，被评为全国高校科技期刊先进集体
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国化学文摘（网络版）,英国农业与生物科学研究中心文摘,波兰哥白尼索引,德国数学文摘,美国剑桥科学文摘,英国动物学记录,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:5888