# Equivalences of classifying spaces completed at the prime two

## 書誌事項

Equivalences of classifying spaces completed at the prime two

Bob Oliver

（Memoirs of the American Mathematical Society, no. 848）

American Mathematical Society, c2006

## 注記

"Volume 180, number 848 (second of 5 numbers)."

Includes bibliographical references (p. 100-102)

## 内容説明・目次

We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.

Introduction Higher limits over orbit categories Reduction to simple groups A relative version of $\Lambda$-functors Subgroups which contribute to higher limits Alternating groups Groups of Lie type in characteristic two Classical groups of Lie type in odd characteristic Exceptional groups of Lie type in odd characteristic Sproadic groups Computations of $\textrm{lim}^1(\mathcal{Z}_G)$ Bibliography.

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