亏群同构于Z32×Z3的块代数的结构

The Structure of Block Algebra with a Defect Group D≌Z_(3~2)×Z_3

假设G是一个有限群,p是一个固定的素数,B是群G的一个p块,且B的一个亏群为D.在模表示理论中,当块B的亏群D给定时,如何确定块B的结构是一个主要问题.这里块B的结构,是指属于块B的不可约模指标个数以及不可约常指标个数.在G是3-可解的或者亏群D是正规的前提下,给出了亏群D同构于Z32×Z3的块代数结构,计算出了k（B）和l（B）这两个重要的块不变量.

Supposed that G be a finite group and p be a fixed prime number, B is a p-block of group G with defect group D. It is a major problem in modular representation theory to determine the structure of B when the defect group D is given. The structure of B here refers to the number of irreducible modular characters as well as the number of irreducible ordinary characters. The algebraic structure of the block algebra with a defect group D≌Z_(3~2)×Z_3 is given under the premise that G is 3-solvable or the defect group D is normal. The two important invariants associated with the block algebra such as k(B)and l(B) are calculated.