Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some char...Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.展开更多
Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concern...Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concerning G-decorrelated decompositions of functions in l2(G). These G-decorrelated decompositions are obtained using the G-convolution either by the irreducible characters of the group G or by an orthogonal projection onto the matrix entries of the irreducible representations of the group G. Applications of these G-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William’s 6×3?design with 3 treatments. In our example, the underlying group is the symmetric group S3.展开更多
It is a well-known fact that characters of a finite group can give important information about the group＇s structure. Also it was proved by the third author of this article that a finite simple group can be uniquely ...It is a well-known fact that characters of a finite group can give important information about the group＇s structure. Also it was proved by the third author of this article that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost simple group by using less information of its character table, and successfully characterize the almost simple K3-groups by their orders and at most three irreducible character degrees of their character tables.展开更多
For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order...For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order to obtain faster speed we modify the algorithm to compute the irreducible characters.展开更多
基金supported by NSFC(12071484)Hunan Provincial Natural Science Foundation(2020JJ4675)Foundation of Guangdong University of Science and Technology.
文摘Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.
文摘Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concerning G-decorrelated decompositions of functions in l2(G). These G-decorrelated decompositions are obtained using the G-convolution either by the irreducible characters of the group G or by an orthogonal projection onto the matrix entries of the irreducible representations of the group G. Applications of these G-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William’s 6×3?design with 3 treatments. In our example, the underlying group is the symmetric group S3.
基金Supported by Natural Science Foundation of China(Grant Nos.11171364,11271301,11471266 and11426182)"the Fundamental Research Funds for the Central Universities"(Grant Nos.XDJK2014C163,XDJK2014C162)+2 种基金Natural Science Foundation Project of CQ CSTC(Grant No.cstc2014jcyj A00010)Postdoctoral Science Foundation of Chongqing(Grant No.Xm2014029)China Postdoctoral Science Foundation(Grant No.2014M562264)
文摘It is a well-known fact that characters of a finite group can give important information about the group＇s structure. Also it was proved by the third author of this article that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost simple group by using less information of its character table, and successfully characterize the almost simple K3-groups by their orders and at most three irreducible character degrees of their character tables.
文摘For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order to obtain faster speed we modify the algorithm to compute the irreducible characters.
