Presentations: from Kac-Moody groups to profinite and back

TL;DR

This paper explores the relationship between presentations of arithmetic and Kac-Moody groups and profinite groups, deriving new insights by translating concepts between these mathematical structures.

Contribution

It introduces novel methods to connect presentations of arithmetic/Kac-Moody groups with those of profinite groups, advancing understanding in both areas.

Findings

New results on group presentations derived from the translation process

Enhanced understanding of the structure of Kac-Moody and profinite groups

Bridging the gap between algebraic and topological group theories

Abstract

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both.