Combinatorial invariants for certain classes of non-abelian groups

2024/08/24 by Godara, Naveen K., Joshi, Renu, Mazumdar, Eshita
#11B75 #11P70 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.13558

Abstract

This article focuses on the study of zero-sum invariants of finite non-abelian groups. We address two main problems: the first centers on the ordered Davenport constant and the second on Gao's constant. We establish a connection between the ordered Davenport constant and the small Davenport constant for a finite non-abelian group of even order, which in turn gives a relation with the Noether number. Additionally, we confirm a conjecture of Gao and Li for a non-abelian group of order 2p^α, where p is a prime. Furthermore, we prove a conjecture that connects the ordered Davenport constant to the Loewy length for certain classes of finite 2-groups.

Related

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• Remarks on a generalization of the Davenport constant
• Davenport constant for finite abelian groups with higher rank
• A classification of finite groups with small Davenport constant
• An application of coding theory to estimating Davenport constants