Glauberman Correspondence of p-Blocks of Finite Groups
Glauberman Correspondence of p-Blocks of Finite Groups
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DOI：
10.1006/jabr.2001.8777
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发表时间：
2001-09
影响因子：
0.9
通讯作者：
Shigeo Koshitani;G. Michler
中科院分区：
文献类型：
--
作者：
Shigeo Koshitani;G. Michler
设G和A是互素阶的有限群。假设A是可解的，它通过自同构作用于G。设C=Cg(A)。用IRR(G)和IRRA(G)分别表示G的所有不可约特征标和所有A-不变不可约特征标的集合。设D≤C是G对素数p的固定p-子群，利用Glauberman对应πG，A：IRR A G→irr C，A.Watanabe(J.Algebra216(1999)，548-565)最近建立了G的A-不变p-块B与缺陷群D和C的P-块B1与缺陷群D之间的Glauberman对应.本文的主要结果是证明了块代数BR(B)和BR(B1)是Morita等价的。此外，如果G是p-可解的，D是交换的，则块代数B和B1是Morita等价的。
Abstract Let G and A be finite groups with coprime orders. Suppose that A is solvable and that it acts on G by automorphisms. Let C = CG(A). By Irr(G) and IrrA(G) we denote the set of all irreducible and all A-invariant irreducible characters of G, respectively. Let D ≤ C be a fixed p-subgroup of G for a prime p. Using the Glauberman correspondence π G , A : Irr A G → Irr C , A. Watanabe (J. Algebra216 (1999), 548–565) recently established a Glauberman correspondence between A-invariant p-blocks B of G with defect group D and p-blocks B1 of C with defect group D. Let Br(B) and Br(B1) be the Brauer correspondents of B and B1 in NG(D) and NC(D), respectively. The main result of this article asserts that the block algebras Br(B) and Br(B1) are Morita equivalent. Furthermore, if G is p-solvable and D is abelian, then the block algebras B and B1 are Morita equivalent.