On the Glauberman and Watanabe correspondences for blocks of finite p-solvable groups
On the Glauberman and Watanabe correspondences for blocks of finite p-solvable groups
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DOI：
10.1090/s0002-9947-02-02990-2
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发表时间：
2002-04
影响因子：
1.3
通讯作者：
M. E. Harris;M. Linckelmann
中科院分区：
文献类型：
--
作者：
M. E. Harris;M. Linckelmann
如果G是素数p的有限p-可解群，A是G的素数阶自同构群|G|的可解子群，使得A稳定G的p-块b并平凡地作用于b的缺陷群P，则块b与其对应的渡边对应w(B)之间存在Morita等价，这是由以ΔP为顶点的双模M和内置换模作为源给出的，这在特征标级上诱导了Glauberman对应(这是渡边结果的同型)。
If G is a finite p-solvable group for some prime p, A a solvable subgroup of the automorphism group of G of order prime to |G| such that A stabilises a p-block b of G and acts trivially on a defect group P of b, then there is a Morita equivalence between the block b and its Watanabe correspondent w(b) of C G (A), given by a bimodule M with vertex ΔP and an endo-permutation module as source, which on the character level induces the Glauberman correspondence (and which is an isotypy by Watanabe's results).