Answer to Question #868 in Complex Analysis for elephant

Question

Find the normalizer of each subgroup of D[sub]2[/sub]

Answer 1

This group have only two elements, one of them is indentity element e - "turn 0 degree" and another element is a - "turn 180 degrees". So this group have only 2 normal trivial subgroup: G and I={e}. From here normalizer is all group G for each subgroup.