PROBABILISTIC METHODS IN GROUP THEORY II

Dedicated to the memory of A. Rcenyi. Introduction. Let (G,+) be a finite Abelian group of order n, and suppose we choose k arbitrary elements gl,g2,"-,gk of G. Let us consider the2 k sums elg 1 + e2g 2 +... + ekg k where each e i = 0 or 1. Two interesting questions present themselves: can every g E G be represented in the form g = elg 1 +... + ekgk, and if so, does each g have about the same number of representations