  We perform an analytical and numerical study of the phase transitions in
three-dimensional Z(N) lattice gauge theories at finite temperature for N>4
exploiting equivalence of these models with a generalized version of the
two-dimensional vector Potts models in the limit of vanishing spatial coupling.
In this limit the Polyakov loops play the role of Z(N) spins. The effective
couplings of these two-dimensional spin models are calculated explicitly. It is
argued that the effective spin models have two phase transitions of BKT type.
This is confirmed by large-scale Monte Carlo simulations. Using a cluster
algorithm we locate the position of the critical points and study the critical
behavior across both phase transitions in details. In particular, we determine
various critical indices, compute the helicity modulus, the average action and
the specific heat. A scaling formula for the critical points with N is
proposed.
