# The diameter of products of finite simple groups

## TL;DR

This paper proves that the diameter of a product of finite simple groups is linearly bounded by the maximum diameter of its factors, providing explicit bounds and including abelian cases for completeness.

## Contribution

It establishes a linear bound on the diameter of products of finite simple groups, extending previous suggestions and including explicit constants for all cases.

## Key findings

- Diameter of product groups is linearly bounded by maximum factor diameter
- Explicit bounds are provided for all cases, including abelian groups
- Includes the case of abelian factors for completeness

## Abstract

Following partially a suggestion by Pyber, we prove that the diameter of a product of non-abelian finite simple groups is bounded linearly by the maximum diameter of its factors. For completeness, we include the case of abelian factors and give explicit constants in all bounds.