Assignment:
Consider the group (reals under addition) and its normal subgroups Z (integers) and Q (rationals 0). (These are normal because R is abelian, of course.)
(i) Find an element of Q/Z of order 350.
(ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the definitions and stay focussed; in particular, pay attention to the definition of a rational number.
(iii) Show that R/Q is torsion free. Think carefully about the elements of R that are not in Q here.
Provide complete and step by step solution for the question and show calculations and use formulas.