Davenport constant for finite abelian groups with higher rank

2024/02/15 by Anamitro Biswas, Biswas, Anamitro, Eshita Mazumdar +1
Engineering · Mathematics · #11B75 #11P99 #20K01 #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.09999

openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite abelian group G, the Davenport Constant, denoted by D(G), is defined to be the least positive integer k such that every sequence of length at least k has a non-trivial zero-sum subsequence. A long-standing conjecture is that the Davenport constant of a finite abelian group G =C_n1×⋯× C_nd of rank d ∈ ℕ is 1+∑_i=1^d (n_i-1) . This conjecture is false in general, but it remains to know for which groups it is true. In this paper, we consider groups of the form G = (C_p)^d-1 × C_pq, where p is a prime and q∈ ℕ and provide sufficient condition when the conjecture holds true.

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