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- W2949203497 abstract "We define a notion of complexity for modules over infinite groups. We show that if $M$ is a module over the group ring $kG$, and $M$ has complexity $leq f$ (where $f$ is some complexity function) over some set of finite index subgroups of $G$, then $M$ has complexity $leq f$ over $G$ (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group $G$ is finite then the complexity of $M$ over $G$ is the maximal complexity of $M$ over an elementary abelian subgroup of $G$. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear groups, $SL(n,Z)$, where $ngeq 2$." @default.
- W2949203497 created "2019-06-27" @default.
- W2949203497 creator A5000210373 @default.
- W2949203497 date "2010-06-01" @default.
- W2949203497 modified "2023-09-27" @default.
- W2949203497 title "Projective resolutions for modules over infinite groups" @default.
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