Question
Asked Sep 28, 2019
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1*. Let f G
H be a group homomorphism. Prove:
(a) If l is the identity of G then /(lg) is the identity of H
(b) If x E G then f(x1) = f(x)-1
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1*. Let f G H be a group homomorphism. Prove: (a) If l is the identity of G then /(lg) is the identity of H (b) If x E G then f(x1) = f(x)-1

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Expert Answer

Step 1

To prove the required properties of a group homomorphism

Step 2
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fGH,hom omorphism,so f(xy) f(x)(yVx, y G. () (a)let x yl in (l) fl)f()) (by uniqueness of identity in Hand cancellation property)

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