Fibered $p$-biset functor structure of the fibered Burnside rings

TL;DR

This paper analyzes the structure of fibered Burnside rings for p-groups over fields with specific characteristics, revealing their composition factors and uniserial nature.

Contribution

It determines the composition factors of the fibered Burnside functor for p-groups and proves its uniseriality in this setting.

Findings

Identifies composition factors of the fibered Burnside functor for p-groups.

Shows the functor is uniserial when the fiber group is cyclic.

Provides structural insights into fibered Burnside rings.

Abstract

We determine the composition factors of the $A$-fibered Burnside functor $kB^A$ for $p$-groups over a field $k$ of characteristic $q$ with $q\neq p$ and cyclic fiber group $A$. We also show that, in this case, $kB^A$ is uniserial.