The author carries out a detailed study of p-blocks with normal metacyclic defect groups provided that p is odd and the defect groups are splitting and nonabelian.In particular,the author constructs all the irreducibl...The author carries out a detailed study of p-blocks with normal metacyclic defect groups provided that p is odd and the defect groups are splitting and nonabelian.In particular,the author constructs all the irreducible ordinary and modular characters in this type of blocks.As a by-product,k(B) and l(B) are obtained.展开更多
Let G be a finite group and let p be a fixed prime number. Let B be a p-block of G with defect group D. In this paper, we give results on 3-blocks with abelian defect groups isomorphic to Z3m ×Z3n. We are particu...Let G be a finite group and let p be a fixed prime number. Let B be a p-block of G with defect group D. In this paper, we give results on 3-blocks with abelian defect groups isomorphic to Z3m ×Z3n. We are particularly interested in the number of irreducible ordinary characters and the number of irreducible Brauer characters in the block. We calculate two important block invariants k（B） and l（B） in this case.展开更多
We first determine in this paper the structure of the generalized Fitting subgroup F＊ （G） of the finite groups G all of whose defect groups （of blocks） are conjugate under the automorphism group Aut（G） to eithe...We first determine in this paper the structure of the generalized Fitting subgroup F＊ （G） of the finite groups G all of whose defect groups （of blocks） are conjugate under the automorphism group Aut（G） to either a Sylow p-subgroup or a fixed p-subgroup of G. Then we prove that if a finite group L acts transitively on the set of its proper Sylow p-intersections, then either L/Op（L） has a T.I. Sylow p-subgroup or p = 2 and the normal closure of a Sylow 2-subgroup of L/O2（L） is 2-nilpotent with completely descripted structure. This solves a long-open problem. We also obtain some generalizations of the classic results by Isaacs and Passman on half-transitivity.展开更多
Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs＇ approach to block structure. We consid...Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs＇ approach to block structure. We consider the block B of a group G as a union of two sets, namely a set of irreducible ordinary characters of G having cardinality k（B） and a set of irreducible Brauer characters of G having cardinality l（B）. We calculate k（B） and l（B） provided that D is normal in G and D = （x, y, z｜x3n=y3m = z3 = [x, z] = [y, z] = 1, [x, y] = z） （n 〉 m 〉 2）.展开更多
We use the method of local representation and original method of Brauer to study the block with K(B) - L(B) = 1, and get some properties on the defect group and the structure of this kind of blocks. Then,we show that ...We use the method of local representation and original method of Brauer to study the block with K(B) - L(B) = 1, and get some properties on the defect group and the structure of this kind of blocks. Then,we show that K(B) conjecture holds for this kind of blocks.展开更多
In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and...In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and only if they are conjugate to each other in G; the number of conjugacy classes whose p-partis contained in P by conjugacy is not larger than |P|.展开更多
The objective of this research paper is to study numerical relationships between a block of a finite group and a defect group of such block. We define a new notion which is called a strongly k(D)- block and give a nec...The objective of this research paper is to study numerical relationships between a block of a finite group and a defect group of such block. We define a new notion which is called a strongly k(D)- block and give a necessary and sufficient condition of a block with a cyclic defect group to be a k(D) -block in term of its inertial index. We believe that the notion and the results in this work will contribute to the developments of the theory of blocks of finite groups.展开更多
文摘The author carries out a detailed study of p-blocks with normal metacyclic defect groups provided that p is odd and the defect groups are splitting and nonabelian.In particular,the author constructs all the irreducible ordinary and modular characters in this type of blocks.As a by-product,k(B) and l(B) are obtained.
文摘Let G be a finite group and let p be a fixed prime number. Let B be a p-block of G with defect group D. In this paper, we give results on 3-blocks with abelian defect groups isomorphic to Z3m ×Z3n. We are particularly interested in the number of irreducible ordinary characters and the number of irreducible Brauer characters in the block. We calculate two important block invariants k（B） and l（B） in this case.
文摘We first determine in this paper the structure of the generalized Fitting subgroup F＊ （G） of the finite groups G all of whose defect groups （of blocks） are conjugate under the automorphism group Aut（G） to either a Sylow p-subgroup or a fixed p-subgroup of G. Then we prove that if a finite group L acts transitively on the set of its proper Sylow p-intersections, then either L/Op（L） has a T.I. Sylow p-subgroup or p = 2 and the normal closure of a Sylow 2-subgroup of L/O2（L） is 2-nilpotent with completely descripted structure. This solves a long-open problem. We also obtain some generalizations of the classic results by Isaacs and Passman on half-transitivity.
基金Supported by National Natural Science Foundation of China(Grant No.13101193)Zhejiang Natural Science Foundation(Grant No.LY16A010016)
文摘Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs＇ approach to block structure. We consider the block B of a group G as a union of two sets, namely a set of irreducible ordinary characters of G having cardinality k（B） and a set of irreducible Brauer characters of G having cardinality l（B）. We calculate k（B） and l（B） provided that D is normal in G and D = （x, y, z｜x3n=y3m = z3 = [x, z] = [y, z] = 1, [x, y] = z） （n 〉 m 〉 2）.
基金supported by the National Natural Seience Foundation of China(Grant Na.19831070)and RFDP.
文摘We use the method of local representation and original method of Brauer to study the block with K(B) - L(B) = 1, and get some properties on the defect group and the structure of this kind of blocks. Then,we show that K(B) conjecture holds for this kind of blocks.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19831070) and BNSF (1992003).
文摘In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and only if they are conjugate to each other in G; the number of conjugacy classes whose p-partis contained in P by conjugacy is not larger than |P|.
文摘The objective of this research paper is to study numerical relationships between a block of a finite group and a defect group of such block. We define a new notion which is called a strongly k(D)- block and give a necessary and sufficient condition of a block with a cyclic defect group to be a k(D) -block in term of its inertial index. We believe that the notion and the results in this work will contribute to the developments of the theory of blocks of finite groups.
