Diameter of a direct power of a finite group

TL;DR

This paper investigates conjectures about the diameter of direct powers of finite groups, proposing bounds related to group size and rank, and provides supporting evidence for these conjectures.

Contribution

It introduces two conjectures on the diameter bounds of G^n with respect to generating sets and offers evidence supporting these conjectures.

Findings

Proposed bounds for the diameter of G^n

Evidence supporting the conjectures

Insights into generating sets and diameters

Abstract

We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of G^n with respect to any generating set is at most n(|G|-rank(G)); and the second one states that there exists a generating set A, of minimum size, for G^n such that the diameter of G^n with respect to A is at most n(|G|-rank(G)). We will establish evidence for each of the above mentioned conjectures.