B(i), (iii), (iv)(ii), (iii), (iv)(i), (ii), (iv)NoneWhich of the following are group homomoprhisms?(i): o: Z₂ → Z₂, 2x² (mod 2).(ii): o: Z→ Z₂, ² (mod 2).(iii): o: Z→ Z3, xx² (mod 3).(iv): : Z→ Z3,2³ (mod 3).

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Answered: Which of the following are group…

Elements Of Modern Algebra

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Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 6E: 6. For each of the following values of , describe all the abelian groups of order , up to...

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D E A D E All (i), (iii), (iv) (ii), (iii), (iv) (i), (ii), (iv) None Which of the following are group homomoprhisms? (i): : Z₂ → Z2, x + x² (mod 2). (ii): o: Z→ Z₂, x→x² (mod 2). (iii): o: Z→ Z3, 2 + x² (mod 3). (iv): o: Z→ Z3,xx³ (mod 3). :
A B D E (i), (ii) (ii), (iv) (iii), (iv) All None Which of the following are ring homomorphisms? (i): f: (2Z, +,-) → (Z,+,-), 3x. (ii): f: (Z8, +,-) → (Z₁, +,-), 2x – 1 (mod 4). (iii): f: (Z8, +,-) → (Z6, +,-), x4x (mod 6). (iv): f: (Z2 x Z5, +,-) → (Z5, +,-), (x,y) →x+y (mod 5) :
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Which of the following are group homomoprhisms? (i): : Z₂ → Z2, x + x² (mod 2). (ii): o: Z→ Z₂, x² (mod 2). (iii): o: Z→ Z3, xx² (mod 3). (iv): o: Z→ Z3,2x³ (mod 3).