Rank, coclass and cohomology

2019/02/07 by Symonds, Peter
#20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1902.02888

Abstract

We prove that for any prime p the finite p-groups of fixed coclass have only finitely many different mod-p cohomology rings between them. This was conjectured by Carlson; we prove it by first proving a stronger version for groups of bounded rank.

Related

• Cohomology of finite p-groups of fixed nilpotency class
• Cohomology of p-groups of nil potency class smaller than p
• The isomorphism problem for graded algebras and its application to mod-p cohomology rings of small p-groups
• The cohomology rings of rank 3 simple groups are Cohen-Macaulay
• Exponents and the cohomology of finite groups