Inverse zero-sum problem of finite abelian groups of rank
Tom 175 / 2024
Colloquium Mathematicum 175 (2024), 77-95
MSC: Primary 11B75; Secondary 11P70
DOI: 10.4064/cm9040-12-2023
Opublikowany online: 5 February 2024
Streszczenie
Let G be a finite abelian group and S be a sequence over G. Let \Sigma _k(S) denote the set of group elements which can be expressed as a sum of a subsequence of S with length k. We study \Sigma _{n^2m}(S) of a sequence S over C_n\oplus C_{nm}, where n,m are positive integers and |S|=n^2m+r with r\in \{nm+n-4,nm+n-3\}. We show that either 0\in \Sigma _{n^2m}(S) or |\Sigma _{n^2m}(S)|\geq (r-nm+3)nm-1. Furthermore, we determine the structure of S if 0\notin \Sigma _{n^2m}(S) and |\Sigma _{n^2m}(S)|= (r-nm+3)nm-1.
