Homotopy equivalences between p-subgroup categories
Copyright policy )Homotopy equivalences between p-subgroup categories
Let p be a prime number and G a finite group of order divisible by p. Quillen showed that the Brown poset of nonidentity p-subgroups of G is homotopy equivalent to its subposet of nonidentity elementary abelian subgroups. We show here that a similar statement holds for the fusion category of nonidentity p-subgroups of G. Other categories of p-subgroups of G are also considered.
19 pages. Second version
- University of Copenhagen Denmark
- University of Copenhagen Denmark
Category of groups, Group Theory (math.GR), Combinatorial aspects of groups and algebras, Partial orders, general, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Combinatorics (math.CO), 05E15 (Primary) 20J15 (Secondary), Mathematics - Group Theory
Category of groups, Group Theory (math.GR), Combinatorial aspects of groups and algebras, Partial orders, general, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Combinatorics (math.CO), 05E15 (Primary) 20J15 (Secondary), Mathematics - Group Theory
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