Diameter of a direct power of a finite group

2015/06/08 by Karimi, Nasim
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1506.02695

Abstract

We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gⁿ 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 Gⁿ such that the diameter of Gⁿ with respect to A is at most n(|G|-rank(G)). We will establish evidence for each of the above mentioned conjectures.

Related

• Diameter of a direct power of alternating groups
• Upper Bounds For The Diameter Of A Direct Power Of Solvable Groups
• On finite groups with polynomial diameter
• On Oriented Diameter of Power Graphs
• Notes on the diameter of the complement of the power graph of a finite group