Assignment:
Let F be a field. The 1-dimensional affine group over F is the set A of all functions f: F → F of the form f(x) = ax+b where a, b belong to F and a is a unit. Let S and T be subsets of A consisting of the scaling (s(x)=ax) and translations (t(x) = x+b)
Are S and T normal subgroups?
If p > 3 and F = Z/p consider the subgroup of D of A generated by T and s(x) = -x. What is the order |D| and can you find an isomorphism of D with a known group?
Provide complete and step by step solution for the question and show calculations and use formulas.