Random Burnside Groups

TL;DR

This paper proves that for sufficiently large odd exponents, random groups are almost surely infinite, extending understanding of group properties in probabilistic models.

Contribution

It establishes the infiniteness of random groups with large odd exponents in both the few relator and density models, a new result in probabilistic group theory.

Findings

Random groups of large odd exponent are infinite with high probability.

The result applies to both the few relator and density models.

Provides new insights into the structure of random Burnside groups.

Abstract

We show that there exists a positive number $M_0$ such that for any odd $M\geq M_0$ a random group of exponent $M$ with overwhelming probability is infinite in the few relator model and in the density $d$ model for small $d$.