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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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

Erratum: Geometry & Topology 9 (2005) 2395–2415

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  Spin7(q) (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(4).

Keywords
Classifying space, $p$–completion, finite groups, fusion.
Mathematical Subject Classification 2000
Primary: 55R35
Secondary: 55R37, 20D06, 20D20
References
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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