ON A CONJECTURE OF ZHUANG AND GAO

Let G be a multiplicatively written finite group. We denote by E(G) the smallest integer t such that every sequence of t elements in G contains a product-1 subsequence of length vertical bar G vertical bar. In 1961, Erdos, Ginzburg and Ziv proved that E(G) <= 2 vertical bar G vertical bar - 1 for every finite abelian group G and this result is known as the Erdos-Ginzburg-Ziv Theorem. In 2005, Zhuang and Gao conjectured that E(G) = d(G) + vertical bar G vertical bar, where d(G) is the small Davenport constant. In this paper, we confirm the conjecture for the case when G = < x, y vertical bar x(p) = y (m) = 1, x(-1) yx = y(r)>, where p is the smallest prime divisor of vertical bar G vertical bar and gcd(p(r - 1), m) = 1.