Cohomology of finite p-groups of fixed nilpotency class

TL;DR

This paper establishes that for fixed prime p, nilpotency class c, and number of generators d, the variety of possible mod p cohomology algebras of finite p-groups is finitely bounded.

Contribution

It proves a bound on the number of isomorphism types of mod p cohomology algebras for finite p-groups with fixed parameters.

Findings

Number of cohomology algebra types is bounded by a function of p, c, and d.

The result applies to d-generated finite p-groups of nilpotency class c.

Provides a finiteness result in the cohomology classification of p-groups.

Abstract

Let p be a prime number and let c, d be natural numbers. Then, the number of possible isomorphism types for the mod p cohomology algebra of a d-generated finite p-group of nilpotency class c is bounded by a function depending only on p, c and d.