Diameter of a direct power of a finite group
Group Theory
2015-10-05 v2
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.
Cite
@article{arxiv.1506.02695,
title = {Diameter of a direct power of a finite group},
author = {Nasim Karimi},
journal= {arXiv preprint arXiv:1506.02695},
year = {2015}
}
Comments
11 pages, extensively revised, unchanged results except proposition 5.9, removed section 5.4