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7. Let G be a group and X be any non-empty subset of G, then necessarily true (A) CelX)= Na(X) (8) ZIG|CCe(X) (C) Ne(HICCa(H) (D) Co(H)CZ[G) 8. G= (+1, t1, tj, tk} group of Quaternion's, then C,conjugacy class of i is (A) (ti} (B) (±1, ti} (C) (+1) (D)仕土k) 9. Let G= (a, ß: a² = B² = (aß)² = e ), then order of a²ß is (A) 1 (C) 3 (D) 6 (B) 2 10. Let (Z, +) be a groups and f: Z-z by f (z) -2, for V zEz, then fis (A) homomorphim only (B) monomorphism only (C) isomorphism (D) empimorphism only

7. Let G be a group and X be any non-empty subset of G, then necessarily true (A) CelX)= Na(X) (8) ZIG|CCe(X) (C) Ne(HICCa(H) (D) Co(H)CZ[G) 8. G= (+1, t1, tj, tk} group of Quaternion's, then C,conjugacy class of i is (A) (ti} (B) (±1, ti} (C) (+1) (D)仕土k) 9. Let G= (a, ß: a² = B² = (aß)² = e ), then order of a²ß is (A) 1 (C) 3 (D) 6 (B) 2 10. Let (Z, +) be a groups and f: Z-z by f (z) -2, for V zEz, then fis (A) homomorphim only (B) monomorphism only (C) isomorphism (D) empimorphism only

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Let G be a group and X be any non-empty subset of G, then necessarily true (A) Ce(X)= Na(X) (8) zIG|CCe(X) (C) Ne(H)Cca(H) (D) CoH)CZ(G) 8. G= {+1, t1, tj. tk} group of Quaternion's, then C,conjugacy class of i is (A) 仕) (B)仕1, 土) (C)土1) (D) (+j, tk } 9. Let G= (a, f: a = B² = (aß)² = e ), then order of a²ß is (A) 1 (B) 2 (C) 3 (D) 6 10. Let (Z, +) be a groups and f: Z-z by f (2) =2, for V zEZ, then fis (A) homomorphim onily (B) monomorphism only (C) isomorphism (D) empimorphism only
Transcribed Image Text:7. Let G be a group and X be any non-empty subset of G, then necessarily true (A) Ce(X)= Na(X) (8) zIG|CCe(X) (C) Ne(H)Cca(H) (D) CoH)CZ(G) 8. G= {+1, t1, tj. tk} group of Quaternion's, then C,conjugacy class of i is (A) 仕) (B)仕1, 土) (C)土1) (D) (+j, tk } 9. Let G= (a, f: a = B² = (aß)² = e ), then order of a²ß is (A) 1 (B) 2 (C) 3 (D) 6 10. Let (Z, +) be a groups and f: Z-z by f (2) =2, for V zEZ, then fis (A) homomorphim onily (B) monomorphism only (C) isomorphism (D) empimorphism only
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