Abstract
In this study, we determine the generalized taxicab group consisting all isometries of the real plane
endowed with the generalized taxicab metric. First we develop natural analogues of Euclidean
reflection and rotation notions, and then determine all isometries in the generalized taxicab plane.
Finally, we show that the generalized taxicab group is semidirect product of the translation group
and the generalized taxicab symmetry group of the unit generalized taxicab circle, as Euclidean
group. We also see that there are transformations of the real plane onto itself which preserve the
generalized taxicab distance, but not preserve the Euclidean distance.