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
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
For a p-block B of a finite group G, we give a bound of the order of its defect group D in terms of k(B), the number of the irreducible ordinary characters in B.
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）.
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.
基金the National Natural Science Foundation of China (Grant No. 10071061) Fujian Province Science Foundation and Mathematical Center of Ministry of Education of China.
文摘For a p-block B of a finite group G, we give a bound of the order of its defect group D in terms of k(B), the number of the irreducible ordinary characters in B.
