# On the Replacement Property for PSL(2, p)

## TL;DR

This paper investigates the replacement property for the group PSL(2, p), providing a complete characterization for primes p > 5, extending previous partial results and deepening understanding of generating sets in these groups.

## Contribution

It offers a comprehensive proof establishing the replacement property for PSL(2, p) when p > 5, filling a gap in the existing literature.

## Key findings

- Complete proof of the replacement property for PSL(2, p) for primes p > 5
- Extension of partial results by Nachman to a full characterization
- Enhanced understanding of generating sets in finite simple groups

## Abstract

The replacement property (or Steinitz Exchange Lemma) for vector spaces has a natural analog for finite groups and their generating sets. For the special case of the groups PSL(2, p), where p is a prime larger than 5, first partial results concerning the replacement property were published by Benjamin Nachman [7]. The main goal of this paper is to provide a complete answer for PSL(2, p).