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
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）.
