#### Volume 6, issue 2 (2002)

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Construction of 2–local finite groups of a type studied by Solomon and Benson

### Ran Levi and Bob Oliver

Geometry & Topology 6 (2002) 917–990
 arXiv: math.AT/0301084
##### Abstract

A $p$–local finite group is an algebraic structure with a classifying space which has many of the properties of $p$–completed classifying spaces of finite groups. In this paper, we construct a family of 2–local finite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2–subgroup of ($q$ an odd prime power) shown by Solomon not to occur as the 2–fusion in any actual finite group. Thus, the resulting classifying spaces are not homotopy equivalent to the $2$–completed classifying space of any finite group. As predicted by Benson, these classifying spaces are also very closely related to the Dwyer–Wilkerson space $BDI\left(4\right)$.

##### Keywords
Classifying space, $p$–completion, finite groups, fusion.
##### Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 55R37, 20D06, 20D20
##### Publication
Received: 22 October 2002
Accepted: 31 December 2002
Published: 31 December 2002
Proposed: Haynes Miller
Seconded: Ralph Cohen, Bill Dwyer
##### Authors
 Ran Levi Department of Mathematical Sciences University of Aberdeen Meston Building 339 Aberdeen AB24 3UE United Kingdom Bob Oliver LAGA – UMR 7539 of the CNRS Institut Galilée Av J-B Clément 93430 Villetaneuse France