  An interesting question about quasiconvexity in a hyperbolic group concerns
finding classes of quasiconvex subsets that are closed under finite
intersections. A known example is the class of all quasiconvex subgroups.
However, not much is yet learned about the structure of arbitrary quasiconvex
subsets. In this work we study the properties of products of quasiconvex
subgroups; we show that such sets are quasiconvex, their finite intersections
have a similar algebraic representation and, thus, are quasiconvex too.
