#### 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

and

LAGA - UMR 7539 of the CNRS, Institut Galilee

Av J-B Clement, 93430 Villetaneuse, France

Email: ran@maths.abdn.ac.uk, bob@math.univ-paris13.fr

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