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有限群的Frobenius谱集合与子群的共轭类型
  • 项目名称：有限群的Frobenius谱集合与子群的共轭类型
  • 项目类别：青年科学基金项目
  • 批准号：11201401
  • 申请代码：A010201
  • 项目来源：国家自然科学基金
  • 研究期限：2013-01-01-2015-12-31
  • 项目负责人：史江涛
  • 依托单位：烟台大学
  • 批准年度：2012
中文摘要：

本项目研究内容分为两部分1.申请人首次引入有限群的Frobenius谱概念，用Frobenius谱集合对有限群作以下深入研究(1)分类Frobenius谱集合具有给定阶或特定算术性质的有限群；(2)仅用所有与群的阶的偶因子相关的Frobenius谱构成的子集合的上确界刻画有限群的可解性，并分类Frobenius谱集合具有给定上确界的有限群；(3)用群的阶和Frobenius谱集合刻画有限群的同构问题；(4)研讨是否任意正整数都可以作为群的Frobenius谱。2.将极大子群的共轭类型概念推广到一般子群(1)深化完善用极大子群共轭类型刻画有限群的可解性和同构问题；(2)用非F-子群的共轭类型刻画有限群的同构问题，这里F表示群类；(3)将(2)的结果推广到仅用非F-子群的共轭类类长集合、同阶类类长集合刻画有限群的同构问题；(4)引入子群共轭类图的概念，用子群共轭类图刻画有限群的同构问题。

中文主题词： 有限群结构；Frobenius谱集合；子群共轭类；TI-子群；正规化子
结论摘要：

英文主题词The structure of finite groups；the set of Frobenius spectrums；conjugacy classes of subgroups；TI-subgroup；normalizer

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 48
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  • 0
  • 0
  • 0
期刊论文
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
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
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
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
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）
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