Generalized prime graphs and the structure of finite groups.

广义素图和有限群的结构。

• 批准号: 22540023
• 负责人: IIYORI Nobuo
• 金额: $ 1.66万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540023/
• 关键词: 有限群; 単純群; 素数グラフ; クイヴァ; 束; ホモロジー; prime graph; バーンサイド環; 部分群束

Let P be a group property and let G be a finite group. The generalized prime graph Γ of G associated with P, or simply theP-graph of G, is a graph whose vertex set is π(G). Two vertices p,q of Γare joined by an edge if and only if there exists a P-subgroup of G whose order is divisible by pq. There are deep relations between the structure of P-graphs and the one of P-subgroup lattices L(G,P) of G. In our research we study the structure of P-subgroup lattice (or group) from point of view of P-graphs. We define a new algebra UD(Q) for a quiver Q and we study UD(L(G,P)). We also find some relations between the structure of G and the one of UD(L(G,P)) and determine the structure of UD(Q) for some quiver Q completely.

设P是群性质，设G是有限群。G与P的广义素数图Γ，或简称为G的P图，是顶点集为π(G)的图。两个顶点p，q （Γare）由一条边连接当且仅当存在G的p -子群其阶能被pq整除。P-图的结构与G的P-子群格的结构L（G，P）之间存在着深刻的联系。本文从P-图的角度研究了P-子群格（或群）的结构。为颤振Q定义了一个新的代数UD(Q)，并研究了UD（L(G，P)）。我们还发现了G和UD（L(G，P)）的结构之间的一些关系，并完整地确定了某些颤振Q的UD(Q)的结构。

项目成果

A theorem on monomials over groups and the classification of finite simple groups

群上的单项式定理和有限单群的分类

• 发表时间: 2011
• 作者: 飯寄信保

A theorem of monomials over groups and the classification of finite groups

群上的单项式定理和有限群的分类

• 发表时间: 2011

Centralizers of p-elements of a finite group.

有限群的 p 元素的集中器。

• 发表时间: 2010
• 作者: 飯寄信保;飯寄信保
• 通讯作者: 飯寄信保

Prime graphs and subgroup lattices of finite groups

有限群的素图和子群格

• 发表时间: 2013