# 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.

## Key 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 $d$.

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Source: https://tomesphere.com/paper/1705.08060