B (ii), (iii) (i), (ii) (i) (iv) (i), (iv) Suppose f: A B is a non-zero group homomorphism. Which of the following are true? (i): If A = Z36, B = Zo, f(2)=4, then f(10) = 2. (ii): If A = B = Z20, f (7) = 9, then f(1) = 6. (iii): If f is an isomorphism, then ker(f) # {e}. (iv): If A = U10, B = Z4, f(3) = 2, then ker(f) = {1}.

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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B
(ii), (iii)
(i), (ii)
(i)
(iv)
(i), (iv)
Suppose f: A B is a non-zero group homomorphism.
Which of the following are true?
(i): If A=Z36, B = Ze, f(2)=4, then f(10) = 2.
(ii): If A = B = Z20, f (7) = 9, then f(1) = 6.
(iii): If f is an isomorphism, then ker(f) # {e}.
(iv): If A = U10, B = Z4, f(3) = 2, then ker(f) = {1}.
Transcribed Image Text:B (ii), (iii) (i), (ii) (i) (iv) (i), (iv) Suppose f: A B is a non-zero group homomorphism. Which of the following are true? (i): If A=Z36, B = Ze, f(2)=4, then f(10) = 2. (ii): If A = B = Z20, f (7) = 9, then f(1) = 6. (iii): If f is an isomorphism, then ker(f) # {e}. (iv): If A = U10, B = Z4, f(3) = 2, then ker(f) = {1}.
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