Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum

Let S = (a(1)) ... (a(k)) be a minimal zero-sum sequence over a finite cyclic group G. The index conjecture states that if k = 4 and gcd(vertical bar G vertical bar, 6) = 1, then S has index 1. In this note we study the index conjecture and connect it to a Dedekind-type sum. In particular we reprove a special case of the conjecture when vertical bar G vertical bar is prime. (C) 2016 Elsevier Inc. All rights reserved.