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Azizolah Azad

Azizolah Azad

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-7950-0977
Education: PhD.
ScopusId: 14420904600
HIndex: 0/00
Faculty: Science
Address: Arak University
Phone:

Research

Title
Upper bounds for the diameter of a direct power of non‑abelian solvable groups
Type
JournalPaper
Keywords
Diameter of a fnite group · Solvable groups
Year
2024
Journal São Paulo Journal of Mathematical Sciences
DOI
Researchers Azizolah Azad ، Nasim Karimi

Abstract

Consider G as a fnite group with a generating set A. We defne the (symmetrice diameter of G with respect to A as the maximum length of the shortest word in (A ∪ A−1)A 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 to denote the n-th direct power of G. For any fnite nonabelian solvable group G and n ≥ 1, we establish an upper bound for both the symmetric diameter and the diameter of Gn. This upper bound grows polynomially with respect to n