Find normalizer and centralizer of the subset H = {1, r2 , r2 s} of the group D5= The dihedral group of order 10.

How do you interprete the main theorem of Galois Thoery in terms of subgroup and subfield diagrams?

Exercise 2.2. Let (G, *) be a group satisfying that (a* b)² = a² * 62 for every a, b = G. Show that G is abelian. Extended quesion* (Opt): What happens if the condition is replaced by (a + b)³ = a³ * 6³?

Consider a dihedral group D4 = 1.Find all the conjugacy classes of D4. Give the detail of your work 2. Discuss all the possible commutators of D4 and verify that 1st derived subgroup of D4 = D4' = [1,a^2]