On stable cohomology of central extensions of elementary abelian groups

TL;DR

This paper investigates the conditions under which kernels of inflation maps in stable cohomology of central extensions of elementary abelian groups are generated by degree two elements, revealing prime size dependencies.

Contribution

It provides new insights into the generation of kernels in stable cohomology for extraspecial p-groups, highlighting when they are generated by degree two components.

Findings

Kernels are generated by degree two components when the prime is large enough.

The generation property fails for smaller primes.

Prime size relative to the rank influences the structure of the kernels.

Abstract

We study when kernels of inflation maps associated to extraspecial p-groups in stable group cohomology are generated by their degree two components. This turns out to be true if the prime is large enough compared to the rank of the elementary abelian quotient, but false in general.