On lengths on semisimple groups

TL;DR

This paper proves that for simple groups over locally compact fields, any length function is either bounded or proper, clarifying the behavior of such functions in these groups.

Contribution

It establishes a dichotomy for length functions on simple groups over locally compact fields, showing they are either bounded or proper.

Findings

Length functions are either bounded or proper on these groups.

Provides a classification of length functions in the context of simple groups over locally compact fields.

Enhances understanding of the geometric structure of such groups.

Abstract

We prove that every length on a simple group over a locally compact field, is either bounded or proper.