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arXiv · 2211.08699

Upper Bounds For The Diameter Of A Direct Power Of Solvable Groups

Azizollah Azad·Nasim Karimi
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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.

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Azizollah Azad, Nasim Karimi. 2022-11-16. Upper Bounds For The Diameter Of A Direct Power Of Solvable Groups. https://arxiv.org/abs/2211.08699

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