On Zero-Sum Subsequences in Finite Abelian Groups
Wolfgang Alexander Schmid · 2001
Let G be a finite abelian group and k ∈ N with $k ot | exp(G)$. Then Ek(G) denotes the smallest integer l ∈ N such that every sequence S ∈ F(G) with |S| ≥ l has a zero-sum subsequence T with $k ot | |T|$. In this paper we prove that if G = Cn1 ⊕···⊕ Cnr is a p-group, k ∈ N with $k ot | exp(G)$ and gcd(p, k) = 1, then Ek(G) = \lfloor \frac{k}{k-1}\sum_{i=1}^r (ni-1) \rfloor+ 1.