Diameter of a direct power of a finite group

DOI10.1080/00927872.2017.1287266zbMATH Open1388.20040arXiv1506.02695OpenAlexW2244713825MaRDI QIDQ4594754

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Publication date: 24 November 2017

Published in: Communications in Algebra (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1506.02695

zbMATH Keywords

diameterrankfinite groupgenerating setdirect power

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