Geometry & Topology 6 (2002) 917–990

DOI: 10.2140/gt.2002.6.917

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

Primary: 55R35

Secondary: 20D06, 20D20, 55R37

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