IIT JAM Follow
December 3, 2020 3:20 pm 30 pts
6. Let G be an Abelian group, then normalizer ofa, N (a) is given by 6. (A) N(a)- {e) (B) N(a)= G (C) N (a)- {e, a} (D) None of these 7. Let G be a group and Z (G) and N (a) are center of G and normalizer of a. Which of the following is true ? (A) aeZ(G) N(a) = G (B) N(a)= Ga.e Z (G) (C) Both (A) and (B) (D) None of these 8. LetG be a finite group and Z (G) be the center of G. Then the class equation of G is given by: o(G) (A) o (G)=o (Z(G) + oeZ[o) o(N (a)) (B) o (G)=o (Z(G) - o(G) aez(G) o(N(a)) o(G) acz[c)o(N(a) (C) o (G)=o (Z(G) +2 (D) None of these Let G be a group of order p for some prime p. Then choose the correct statement: (A) Z (G)= {e} (B) Z (G) {e) D) None of these (C) Z (G) = G 10. Let G= , Gi = be two cyclic groups of order m and n such that (m, n)> 1. Then Gi x Gz is: (B) Abelian as well as eyclic (A) Abelian but not cyclic (D) None of these (C) Cyclic but not Abelian (3) niATI6