On some weighted zero-sum constants II

Abstract

For a finite abelian group G with exponent n, let A = {a ∈ ℤ:gcd(a,n) = 1}. The constant sA(G) (respectively ηA(G)) is defined to be the least positive integer t such that given any sequence S over G with length |S|≥ t has a A-weighted zero-sum subsequence of length n (respectively at most n). In [M. N. Chintamani and P. Paul, On some weighted zero-sum constants, Int. J. Number Theory 13(2) (2017) 301-308], we proved the exact value of this constant for the group ℤpα ⊕ ℤp and proved the structure theorem for the extremal sequences related to this constant. In this paper, we prove the similar results for the group ℤpα ⊕ ℤp2 and we obtained an upper bound when pα is replaced by any integer n ≥ 2.