There is no upper bound for the diameter of the commuting graph of a finite group

TL;DR

This paper constructs a family of finite special 2-groups demonstrating that the diameter of their commuting graphs can grow without bound, challenging previous assumptions about such graph properties.

Contribution

It introduces a new family of finite special 2-groups with unbounded commuting graph diameters, providing counterexamples to existing bounds.

Findings

Commuting graph diameter can be arbitrarily large.

Constructed specific examples of finite special 2-groups.

Challenged previous bounds on commuting graph diameters.

Abstract

We construct a family of finite special 2-groups which have commuting graph of increasing diameter