Upper bounds for the diameter of a direct power of non-abelian solvable groups

Consider G as a finite group with a generating set A. We define the (symmetric) diameter of G with respect to A as the maximum length of the shortest word in (A boolean OR A-1)A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \cup A<^>{-1}) A$$\end{document} expressing g, where g ranges over all elements in G. The (symmetric) diameter of G is then the maximum (symmetric) diameter over all possible generating sets of G. We use Gn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G<^>n$$\end{document} to denote the n-th direct power of G. For any finite non-abelian solvable group G and n >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 1$$\end{document}, we establish an upper bound for both the symmetric diameter and the diameter of Gn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G<^>n$$\end{document}. This upper bound grows polynomially with respect to n.