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In this paper we look at a special type of discrete subgroups of$PSL_{n+1}(\Bbb{C})$ called Schottky groups. We develop some basic propertiesof these groups and their limit set when $n > 1$, and we prove that Schottkygroups only occur in odd dimensions, {\it i.e.}, they cannot be realized assubgroups of $PSL_{2n+1}(\Bbb{C})$.

Schottky groups cannot act on $\mathbb{P}^{2n}_{\mathbb{C}}$ as subgroups of $PSL(2n+1,\Bbb{C})$