## Geometry & Topology

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

#### 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 $BDI(4)$.

#### Article information

Source
Geom. Topol., Volume 6, Number 2 (2002), 917-990.

Dates
Accepted: 31 December 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882943

Digital Object Identifier
doi:10.2140/gt.2002.6.917

Mathematical Reviews number (MathSciNet)
MR1943386

Zentralblatt MATH identifier
1021.55010

#### Citation

Levi, Ran; Oliver, Bob. Construction of 2–local finite groups of a type studied by Solomon and Benson. Geom. Topol. 6 (2002), no. 2, 917--990. doi:10.2140/gt.2002.6.917. https://projecteuclid.org/euclid.gt/1513882943

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