A relative version of Webb's theorem on the equivariant chain complex of a subgroup complex

Peter Symonds

doi:10.1016/j.jpaa.2007.12.009

A relative version of Webb's theorem on the equivariant chain complex of a subgroup complex

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Abstract

We prove a relative version of the theorem of Webb that the augmented chain complex of the p-subgroup complex of a finite group, considered as a complex of modules for the group, is homotopy equivalent to a complex of projectives. This allows us to take into account the group of automorphisms of the group. © 2008 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1984-1986
Number of pages	2
Journal	Journal of Pure and Applied Algebra
Volume	212
Issue number	8
DOIs	https://doi.org/10.1016/j.jpaa.2007.12.009
Publication status	Published - Aug 2008

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title = "A relative version of Webb's theorem on the equivariant chain complex of a subgroup complex",

abstract = "We prove a relative version of the theorem of Webb that the augmented chain complex of the p-subgroup complex of a finite group, considered as a complex of modules for the group, is homotopy equivalent to a complex of projectives. This allows us to take into account the group of automorphisms of the group. {\textcopyright} 2008 Elsevier Ltd. All rights reserved.",

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AB - We prove a relative version of the theorem of Webb that the augmented chain complex of the p-subgroup complex of a finite group, considered as a complex of modules for the group, is homotopy equivalent to a complex of projectives. This allows us to take into account the group of automorphisms of the group. © 2008 Elsevier Ltd. All rights reserved.

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DO - 10.1016/j.jpaa.2007.12.009

M3 - Article

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SP - 1984

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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A relative version of Webb's theorem on the equivariant chain complex of a subgroup complex

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