Geometry & Topology

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

Ran Levi and Bob Oliver

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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).

Article information

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

Received: 22 October 2002
Accepted: 31 December 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 55R37: Maps between classifying spaces 20D06: Simple groups: alternating groups and groups of Lie type [See also 20Gxx] 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure

Classifying space $p$–completion finite groups fusion.


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.

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