Let G1 be the group generated by a nonzero translation and G2 be the group generated by a glide reflection. Show that G1 and G2 are isomorphic. Here is how I started: G1 = <Tb> where b[tex]\in[/tex] C and Tb(z) = z+b G2 = <ML [tex]\circ[/tex] Tc> where c and L are parallel to each other. Let's define a function [tex]\Phi[/tex]: G1 [tex]\rightarrow[/tex] G2 Then if [tex]\Phi[/tex] is a homomorphism and a bijection, it is an isomorphism. But here lies my problem, I do not know what to make [tex]\Phi[/tex] equal to. Maybe this isn't the right way of approaching this problem. Thanks in advance.