It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abel...It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abelian normal {p, q} complement A, and the centralizer in A of the Sylow p-subgroup of G is equal to the centralizer in A of the Sylow q-subgroup of G.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
In 1984, Isaacs proposed the theories of Bπ-character and Iπ-character in π-separated group. This paper gives some new extension conditions of Iπ characters.
Strict proof has been given to single valley character of level degree function by use of convex analysis theory, which provides reliable theoretical basis for the optimization of the data processing with respect to l...Strict proof has been given to single valley character of level degree function by use of convex analysis theory, which provides reliable theoretical basis for the optimization of the data processing with respect to level degree. As circle degree and cylindrical degree have the same mathematical structures, their single valley character can be proved by the same method.展开更多
设p为奇质数,q=p^(n)(n∈Z^(+)),f(x)∈F_(q)[x].Wan(Journal of Systems Science and Complexity,2021,34(4):498-510.)研究了指数和S_(q)(f(x))的代数次数及周期性.特别地,陈超等(四川大学学报(自然科学版),2020,57(6):1029-1032.)证...设p为奇质数,q=p^(n)(n∈Z^(+)),f(x)∈F_(q)[x].Wan(Journal of Systems Science and Complexity,2021,34(4):498-510.)研究了指数和S_(q)(f(x))的代数次数及周期性.特别地,陈超等(四川大学学报(自然科学版),2020,57(6):1029-1032.)证明了p≡-1(mod d)且q=p^(2)时,S_(q)(x^(d))=-p或(d-1)p.基于上述结果,讨论p≡-1(mod d)且q=p^(2r)(r∈Z^(+))时S_(q)(x^(d))的具体取值,进而利用初等的方法和技巧,得到deg S_(q)(x^(d))=1时,S_(q)(x^(d))的全部可能取值.展开更多
It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined b...It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author 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 automorphism groups of Mathieu groups by their orders their character tables. and at most two irreducible character degrees of展开更多
文摘It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abelian normal {p, q} complement A, and the centralizer in A of the Sylow p-subgroup of G is equal to the centralizer in A of the Sylow q-subgroup of G.
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.
基金Supported by the Education Hall Foundation of Zhejiang Province(20051313)
文摘In 1984, Isaacs proposed the theories of Bπ-character and Iπ-character in π-separated group. This paper gives some new extension conditions of Iπ characters.
文摘Strict proof has been given to single valley character of level degree function by use of convex analysis theory, which provides reliable theoretical basis for the optimization of the data processing with respect to level degree. As circle degree and cylindrical degree have the same mathematical structures, their single valley character can be proved by the same method.
文摘设p为奇质数,q=p^(n)(n∈Z^(+)),f(x)∈F_(q)[x].Wan(Journal of Systems Science and Complexity,2021,34(4):498-510.)研究了指数和S_(q)(f(x))的代数次数及周期性.特别地,陈超等(四川大学学报(自然科学版),2020,57(6):1029-1032.)证明了p≡-1(mod d)且q=p^(2)时,S_(q)(x^(d))=-p或(d-1)p.基于上述结果,讨论p≡-1(mod d)且q=p^(2r)(r∈Z^(+))时S_(q)(x^(d))的具体取值,进而利用初等的方法和技巧,得到deg S_(q)(x^(d))=1时,S_(q)(x^(d))的全部可能取值.
基金supported by the National Natural Science Foundation of China(Nos.11426182,11401324,11271301,11471266,10871032)SRF for ROCS,SEM,the Fundamental Research Funds for the Central Universities(No.SWU115052)+1 种基金the Natural Science Foundation Project of CQ CSTC(Nos.cstc2014jcyj A00010,cstc2014jcy A0148,2010BB9206)the National Science Foundation for Distinguished Young Scholars of China(No.11001226)
文摘It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author 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 automorphism groups of Mathieu groups by their orders their character tables. and at most two irreducible character degrees of
