Geometry & Topology, Vol. 6 (2002) Paper no. 28, pages 917--990.

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

Ran Levi, Bob Oliver

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 Spin_7(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).

Note. (9 February 2005) An error in the paper was pointed out to the authors by Andy Chernak. The error is corrected in the erratum which should be read alongside the original version of the paper.

Keywords. Classifying space, p-completion, finite groups, fusion.

AMS subject classification. Primary: 55R35. Secondary: 55R37, 20D06, 20D20.

DOI: 10.2140/gt.2002.6.917

E-print: arXiv:math.AT/0301084

Submitted to GT on 22 October 2002. Paper accepted 31 December 2002. Paper published 31 December 2002. Erratum published 9 February 2005.

Erratum Notes on file formats

Ran Levi, Bob Oliver
Department of Mathematical Sciences, University of Aberdeen
Meston Building 339, Aberdeen AB24 3UE, UK
LAGA - UMR 7539 of the CNRS, Institut Galilee
Av J-B Clement, 93430 Villetaneuse, France


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