Answer to Question #218544 in Abstract Algebra for Rabia qadeer

Question

If the following are true, give detailed proof. Otherwise, support your answer by a

nontrivial example. { same example by all students may lead to -ve marking }

(i) S4 is isomorphic to D12.

(ii) H ∼

= K if and only if Aut(H) ∼

= Aut(K).

(iii) Every action of the group G gives the same orbit space.

(iv) The isomorphism class of the multiplicative group of real numbers is non-empty.

(v) The converse of Cauchy’s theorem is true.