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- W2012202832 abstract "In this paper we present a general view of the role of elementary Abelian subgroups in the representation theory of a finite group G. We show that any G-module M is a direct summand of a module that has a filtration by modules induced from elementary Abelian subgroups. This implies that if we are given any sequence of cohomology elements, such that the product of the elements in the sequence makes sense and that the elements restrict to zero on the elementary Abelian subgroups, then the product of the elements is zero provided the sequence has sufficient length. If the coefficient ring is a field of finite characteristic p, then only the elementary Abelian p-subgroups are relevant. In that case, the theorems of Quillen on the dimension of the mod-p cohomology ring and of Alperin-Evens on the complexity of modules are easy consequences of our results." @default.
- W2012202832 created "2016-06-24" @default.
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- W2012202832 date "2000-06-01" @default.
- W2012202832 modified "2023-09-27" @default.
- W2012202832 title "Cohomology and induction from elementary Abelian subgroups" @default.
- W2012202832 doi "https://doi.org/10.1093/qjmath/51.2.169" @default.
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