Construction of 2-local finite groups of a type studied by Solomon and Benson
85 citations recorded by the source corpus.
A p{local nite group is an algebraic structure with a classifying space which has many of the properties of p{completed classifying spaces of nite groups. In this paper, we construct a family of 2{local nite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2{subgroup of Spin7(q )( qan odd prime power) shown by Solomon not to occur as the 2{fusion in any actual nite group. Thus, the resulting classifying spaces are not homotopy equivalent to the 2{completed classifying space of any nite group. As predicted by Benson, these classifying spaces are also very closely related to the Dwyer{Wilkerson space BDI(4).
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/caf27c76f00adc054c5b3aa85617717f3bb126db
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The classification of p-local finite groups over the extraspecial group of order p3 and exponent p (2004, background): “These are the simplest examples of exotic p-local finite groups known so far ([2, Section 9], [8]) and are intensively studied in a sequel paper [12].”
- Simple fusion systems and the Solomon 2-local groups (2006, methodology): “We introduce a notion of simple fusion systems which imitates the corresponding notion for finite groups and show that the fusion system on the Sylow-2subgroup of a 7-dimensional spinor group over a field of characteristic 3 considered by Ron Solomon [18] and by Ran Levi and Bob Oliver [11] is simpl”
- All p-local finite groups of rank two for odd prime p (2004, background): “Unlike the other known infinite families of exotic p-local finite groups [13, 30], some of these new families cannot be constructed as the homotopy fixed points of automorphism of a p-compact group.”