IIT JAM Follow
December 3, 2020 3:09 pm 30 pts
6. 6. Let G be an Abelian group, then normalizer of a, N(a) 15 given by (A) N (a)= {e} (B) N()=G (C) N()= {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) a e Z(G) N(a) = G (B) N(a) =G a.c Z(G) (C) Both (A) and (B) (D) None of these 8 Let G be a finite group and Z (G) be the center of G. Then the class equation of G is given by: (A) o (G) =o (Z(G) +2 o(G) aeZ(G) O(N (a) (B) o (G) =o (Z(G) - o(G) aez[G) o(N(a) o(G) aeZ[a)o(N (a) (C) o (G)=o (Z(G) + A (D) None of thes C 9. 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) (C) Z (G) =G (D) None of these 10. Let G = , Gi be two cyclic groups of order m and n such that (m, n)> 1. Then G1 x Gz is: (B) Abelian as well as éyclic (A) Abelian but not cyclic (D) None of these (C) Cyclic but not Abelian (3) E(H-3)-MAT(6)
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