Research on properties of generating functions for permutation representations and their applications.

排列表示生成函数的性质及其应用研究。

• 批准号: 17540002
• 负责人: TAKEGAHARA Yugen
• 金额: $ 2.39万
• 依托单位: Muroran Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540002/
• 关键词: finitely generated group; profinite group; exponential generating function; nilpotent group; finite abelian group; free product; finite group; Burnside ring; 準同型; 対称群; G集合; Dress's induction theorem; Artin's induction theorem; p進解析関数; 対象群

a) For each natural number n, let G_n be the kernels of certain linear characters of the wreath product of a finite group by the symmetric group S_n on n letters. When A is a finitely generated group or a profinite group, the exponential generating function for the number of homomorphisms from A to G_n is determined.b) For a finite group G, the properties of the function T_n from G to the nonnegative integers such that for each g, T_n (g) is the number of sequences (x_1,x_2,…,x_n) of elements of G satisfying the higher commutator [x_1,x_2,…,x_n]=g are obtained.c) It is obtained that a finite group G is nilpotent of class n if and only if a certain matrix determined from the character table of G is nilpotent of index n.d) A certain congruence equation modulo p for the number of subgroups of index d, d a fixed natural number, in the free product of finite abelian groups is obtained.e) Suppose that a finite group A is an operator group of a finite group G, and consider G as a right A-set. A free right G-set Y is called (A,G)-set if Y is a left A-set with the action given by a(yg)=(ay)^ag, a∈A, y∈Y, g∈G. An (A,G)-set is called simple if it is a transitive A-set. A complete set of representatives of isomorphism classes of simple (A,G)-sets is determined. The Grothendieck ring of the category of the (A,G)-set is defined, and some properties of the Burnside ring of a finite group are generalized. Moreover, an exlicit formula of Brauer's induction theorem is obtained as an application of the theory.

a)对于每个自然数n，设G_n为有限群与对称群S_n在n个字母上的圈积的某些线性特征的核。当A是有限生成群或无限生成群时，确定A到G_n的同态个数的指数生成函数。有限群G b),函数的性质从G T_n非负整数,对于每一个G, T_n (G)是序列的数量(x_1、x_2…,x_n) G的元素满足更高的换向器(x_1、x_2…,x_n) = G obtained.c)是获得一个有限群G的幂零类n当且仅当一个特定的字符表的矩阵确定G是幂零指数无日期)一定的同余方程模p子群的指数d的数量,得到了有限阿贝尔群自由积中的一个固定自然数D。e)设有限群a是有限群G的算子群，并设G为右a集。一个自由的右G集Y称为（A，G）-集，如果Y是一个左A集，其作用为A (yg)=(ay)^ag, A∈A, Y∈Y, G∈G。如果一个（A，G）集是可传递的A集，则称其为简单集。确定了简单（A，G）-集的同构类的代表的完备集。定义了（A，G）-集合范畴的Grothendieck环，推广了有限群Burnside环的一些性质。此外，作为该理论的应用，得到了Brauer归纳定理的一个显式公式。

项目成果

Periodic Solutions of Elliptic-Parabolic Variational Inequalities with Time-Dependent Constraints

• DOI: 10.3934/dcds.2007.19.335
• 发表时间: 2006-02
• 期刊: Journal of Evolution Equations
• 影响因子: 1.4
• 作者: M. Kubo;N. Yamazaki

Extremal self-dual codes of length 64 through neighbors and covering radii Designs

通过邻居和覆盖半径设计的长度为 64 的极值自对偶码

• 发表时间: 2007
• 期刊: Codes and Cryptography 42
• 作者: J.-M.Deshouillers;K.Kawada;T.D.Wooley;川田 浩一;川田 浩一;Koichi Kawada;川田 浩一;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;Y. Takegahara;Naoki Chigira;Naoki Chigira;竹ヶ原 裕元;Naoki Chigira;Naoki Chigira
• 通讯作者: Naoki Chigira

Global solvability of constrained singular diffusion equation associated with essential variation

与本质变差相关的约束奇异扩散方程的全局可解性

• 发表时间: 2006
• 期刊: Free Boundary Problems : Theory and Applications, Int. Series Numer. Math. 154
• 作者: Y.Giga;H.Kuroda;N.Yamazaki
• 通讯作者: N.Yamazaki

Some self-dual codes invariant under the Hall-Janko group

Hall-Janko群下的一些自对偶码不变

• 发表时间: 2007
• 期刊: J. Algebra 316, no.2
• 作者: N. Chigira;M. Harada;M. Kitazume
• 通讯作者: M. Kitazume

Nilpotent groups and character tables

幂零群和字符表

• 发表时间: 2007
• 期刊: 数理解析研究所考究録 1564
• 作者: J.-M.Deshouillers;K.Kawada;T.D.Wooley;川田 浩一;川田 浩一;Koichi Kawada;川田 浩一;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;川田 浩一;Koichi Kawada;Y. Takegahara;Naoki Chigira;Naoki Chigira;竹ヶ原 裕元
• 通讯作者: 竹ヶ原 裕元