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

2023/11/04 by Godara, Naveen K., Sarkar, Siddhartha
#FOS: Mathematics #Group Theory (math.GR) #Primary 20D60 #Secondary 11B75

paper · doi:10.48550/arxiv.2311.02387

Abstract

The small Davenport constant d(G) of a finite group G is defined to be the maximal length of a sequence over G which has no non-trivial product-one subsequence. In this paper, we prove that 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.

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