Upper Bounds For The Diameter Of A Direct Power Of Solvable Groups
Group Theory
2022-11-17 v1
Abstract
Let G be a finite group with a generating set A. By the (symmetric) diameter of G with respect to A we mean the maximum over g in G of the length of the shortest word in (A union A inverse)A expressing g.By the (symmetric) diameter of G we mean the maximum of (symmetric) diameter over all generating sets of G. Let n greater than or equal to 1, by G power n we mean the n-th direct power of G. For n greater than or equal to 1 and finite non-abelian solvable group G we find an upper bound, growing polynomially with respect to n, for the symmetric diameter and the diameter of G power n.
Cite
@article{arxiv.2211.08699,
title = {Upper Bounds For The Diameter Of A Direct Power Of Solvable Groups},
author = {Azizollah Azad and Nasim Karimi},
journal= {arXiv preprint arXiv:2211.08699},
year = {2022}
}
Comments
10 pages. arXiv admin note: substantial text overlap with arXiv:1506.02695