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Item Details
Title: EQUIVALENCES OF CLASSIFYING SPACES COMPLETED AT THE PRIME TWO
By: Bob Oliver (Editor)
Format: Paperback

List price: £61.00


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ISBN 10: 0821838288
ISBN 13: 9780821838280
Publisher: AMERICAN MATHEMATICAL SOCIETY
Pub. date: 15 January, 2006
Series: Memoirs of the American Mathematical Society No. 180
Pages: 102
Description: Proves that 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.
Synopsis: 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.
Publication: US
Imprint: American Mathematical Society
Returns: Returnable
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