A remark on blocks with dihedral defect groups in solvable groups
A remark on blocks with dihedral defect groups in solvable groups
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关于可解群中具有二面缺陷群的块的评论
DOI：
10.1007/bf01215342
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发表时间：
1982
影响因子：
0.8
通讯作者：
Shigeo Koshitani
中科院分区：
文献类型：
--
作者：
Shigeo Koshitani
设F是特征p> 0的代数闭域，G是有限群，FG是G在F上的群代数。设B是FG的块理想（即B是FG的不可分解的双边理想和直和项），其亏群为D. Erdmann和Michler [3]在（*）p= 2，G是可解的，D是二面体的情形下，得到了B中所有投射不可分解FG-模的Loewy因子，本文的目的是确定（*）情形下B的F-代数结构.设G是一个有限可解群，B是FG的一个块理想，其中D的二面体亏群的阶为2n（n> 2），l（B）是B中非同构的单FG-模的个数.则存在整数m> 1，使得以下之一成立;
Let F be an algebraically closed field of characteristic p> 0, G a finite group and FG the group algebra of G over F. Let B be a block ideal of FG (ie B is an indecomposable two-sided ideal and a direct summand of FG) with defect group D. About five years ago Erdmann and Michler [3] obtained the Loewy factors of all projective indecomposable FG-modules in B in the case where (*) p= 2, G is solvable and D is dihedral.The purpose of the present paper is to determine the F-algebra-structure of B in the case (*). This can be stated as follows: Let G be a finite solvable group, let B be a block ideal of FG with dihedral defect group D of order 2 n for some n> 2, and let l (B) be the number of non-isomorphic simple FG-modules in B. Then there is an integer m> 1 such that one of the following holds;