Calculate the commutators u v of various pairs of elements u

Calculate the commutators [u, v] of various pairs of elements u, nuepsilonG = Isom(R). Find a general form for these commutators and so identify the subgroup G\'of G which they generate Thus, every commutator is a translation and (taking c = 0, epsilon = 1) vice versa. Thus G\'=T=G^+

Solution

by given hint it is very straight forword

to write general form of given comutators

as [u,v]=u^n_i v^m_j t(d(1+or- 1)-c(1+or- 1)

is requred solution where n_i and m_j belongs to {0,1,2,3...}