Characters and local structure in G-algebras
Characters and local structure in G-algebras
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DOI：
10.1016/0021-8693(80)90074-5
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发表时间：
1980-04
影响因子：
0.9
通讯作者：
M. Broué;L. Puig
中科院分区：
文献类型：
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作者：
M. Broué;L. Puig
设p是素数，G是有限群.设x是G的ap-块B中的广义特征标.设P是G的Sylowp-子群，T_i是P的广义特征标，使得T（X）=（v），只要P中的x和y在G的一个元素下共轭，则已知（例如，参见[9，定理I]），可以在B中构造另一个广义特征标x* 7，如下：当x是G的p-元时，我们用xw表示G的中心函数，该中心函数在x的p-截面X之外消失，并且其对X的限制等于x的限制，并且我们为G的p-元的共轭类选择P中的代表集S;本文的目的是给出一个更一般的构造，它与[1]中开始的局部方法密切相关。根据[1]，当从给定p-块B的角度研究G时，用研究“（6，G）-Brauer对”（P，e）来代替G的p-子群的研究是有用的，其中P是G的p-子群，e是C的块，（P）与6相关联。人们特别知道[I，定义3.31]如何定义这种（B，G）-Brauer对的“包含”，然后G通过共轭传递地作用在最大的（6，G）-Brauer对上[I，定理3.101]。
Let p be a prime number and let G be a finite group. Let x be a generalized character in ap-block b of G. If P is a Sylowp-subgroup of G and T] is a generalized character of P such that T (X)= &v) whenever x and y in P are conjugate under an element of G, it is well known (see [9, Theorem I], for example) that it is possible to construct another generalized character x* 7 in b, as follows: whenever x is a p-element of G, we denote by xw the central function of G which vanishes outside of the p-section X of x and whose restriction to X is equal to the restriction of x, and we choose a set S of representatives in P for the conjugacy classes of p-elements of G; then, we set x* 7= 1 q (x) p. XESThe aim of this paper is to give a more general construction, closely related to the local methods started in [l]. According to [l], when studying G from the point of view of a given p-block b, it is useful to replace the study of p-subgroups of G by the study of “(6, G)-Brauer pairs”(P, e), where P is a p-subgroup of G and e is a block of C,(P) associated with 6. One knows in particular [I, Definition 3.31 how to define the “inclusion” of such (b, G)-Brauer pairs and then G acts transitively by conjugation on the maximal (6, G)-Brauer pairs [l, Theorem 3.101.