Control of Fusion by Abelian Subgroups of the Hyperfocal Subgroup

2016/11/14 by Henke, Ellen, Liao, Jun
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1611.04403

Abstract

We prove that an isomorphism between saturated fusion systems over the same finite p-group is detected on the elementary abelian subgroups of the hyperfocal subgroup if p is odd, and on the abelian subgroups of the hyperfocal subgroup of exponent at most 4 if p = 2. For odd p, this has implications for mod p group cohomology.

Related

• Control of fusion by elementary abelian subgroups of rank at least 2
• Assigning a classifying space to a fusion system up to F-isomorphism
• Fusion systems over a Sylow p-subgroup of G₂(p)
• A characterization of saturated fusion systems over abelian 2-groups
• Spectra of subrings of cohomology generated by characteristic classes for fusion systems