# Kac-Moody Groups and Completions

## TL;DR

This paper introduces a new pro-p-complete topological Kac-Moody group, compares it with existing groups, and explores conditions under which completions admit BN-pairs, advancing understanding of group completions.

## Contribution

It constructs a novel pro-p-complete topological Kac-Moody group and provides explicit criteria for its completion to admit a BN-pair, linking group completion theory with Kac-Moody groups.

## Key findings

- Constructed a new pro-p-complete topological Kac-Moody group.
- Compared the new group with known topological Kac-Moody groups.
- Established explicit criteria for the completion to admit a BN-pair.

## Abstract

In this paper we construct a new "pro-p-complete" topological Kac-Moody group and compare it to various known topological Kac-Moody groups. We come across this group by investigating the process of completion of groups with BN-pairs. We would like to know whether the completion of such a group admits a BN-pair. We give explicit criteria for this to happen.