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arXiv:2311.02387 [math.GR]AbstractReferencesReviewsResources

A note on a Conjecture of Gao and Zhuang for groups of order $27$

Naveen K. Godara, Siddhartha Sarkar

Published 2023-11-04Version 1

The small Davenport constant ${\mathsf{d}}(G)$ is defined to be the maximal length of a product-one free non-trivial sequence in a finite group $G$. In this paper, we prove that ${\mathsf{d}}(G) = 6$ for the non-abelian group of order $27$ and exponent $3$ and thereby establish a conjecture by Gao and Zhuang for this group.

Categories: math.GR
Subjects: 20D60, 11B75
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