Zassenhaus filtrations as intersections

TL;DR

This paper links Zassenhaus filtrations of profinite groups to representation theory by describing these filtrations as intersections of kernels of specific representations, offering a new perspective on studying such groups.

Contribution

It introduces a novel approach to analyze Zassenhaus filtrations through representation kernels, bridging group filtrations and representation theory.

Findings

Zassenhaus filtrations can be characterized as intersections of kernels of certain representations.

Establishes a new connection between profinite group filtrations and representation theory.

Provides a framework for studying profinite groups using representation-theoretic methods.

Abstract

Zassenhaus filtrations of profinite groups are an important tool to study profinite groups.In this paper, we describe Zassenhaus filtrations of profinite groups as intersections of kernels of certain representations. In this way we introduce a link between studying profinite groups with methods of Zassenhaus filtrations and representation theory.