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Let C2 be the cyclic group of order 2 and D2n be the dihedral group of order 2n, where n is even. In this paper, we provide the exact values of some zero-sum constants over D2n × C2, namely the small Davenport constant, Gao constant, n--constant and Erd\H os--Ginzburg--Ziv constant. As a consequence, we prove Gao's conjecture and the Zhuang--Gao conjecture for this group. These are the first concrete results on zero-sum problems for a family of non-abelian groups of rank greater than two. [ABSTRACT FROM AUTHOR]

Let C2 be the cyclic group of order 2 and D2n be the dihedral group of order 2n, where n is even. In this paper, we provide the exact values of some zero-sum constants over D2n × C2, namely the small Davenport constant, Gao constant, n--constant and Erd\H os--Ginzburg--Ziv constant. As a consequence, we prove Gao's conjecture and the Zhuang--Gao conjecture for this group. These are the first concrete results on zero-sum problems for a family of non-abelian groups of rank greater than two. [ABSTRACT FROM AUTHOR]