  The exact solution of a general Z(4) gauge Potts model with a single and
double plaquette representation of the action is found on a subspace of
gauge-coupling parameters on the square and triangular lattices. The two
Ising-type critical lines of a second-order phase transition for the model on a
square lattice are found. For the model on a triangular lattice the two
critical surfaces of an Ising-type and two nontrivial lines of a second-order
phase transition with different critical behavior than on the critical surfaces
are found. It is shown that a two dimensional (2D) general Z(4) gauge Potts
model with single and double plaquette representation of the action and a 2D
spin-3/2 Ising model belong to the same universality class.
