IIT JAM Follow
December 3, 2020 2:26 pm 30 pts
6. Let G be an Abelian group, then normalizer of a, N)sgken y (A) N () (e) (8) N(a)=G (C) N()(e,o) (D) None af thest 7. Let G be a group and Z (G) and N (a) are center of G and namalier ota hich of the following is true7 (A) ac Z(G)> N(a)-G (B) N(a)-Gsaei (C) Both (A) and (B) (D) None o these 8. Let G be a finite group and Z (G) be the cenner of G. Then the ls equsoe of is given by: o(G) (A) o (G)o(Z0)+ 2 oN uZlo) o(N (a)) o(G) (B) o (G)o (Z(G) OG aZ[o) oN(a)) o(G) ()o(G)o (Z(G)) + oN(a)) oZa) o(N (a)) (D) None of these Let G be a group of order p for some prime het ches 0ret 9 statement (A) Z (G)-(e) B) Z) e (C) Z (G)-G D) None al these 10. Let G, be two cyclic grouns of e an n sach that (i, n)> 1. Then G x Gz is : (A) Abelian but not cyclic B) Abelian as well asee (C) Cyclic but not Abelian (D) None ol these XE(H-3)-MAT(6) (3
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