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We have a group Homomorphism φ which define φ:G--->G' , and His subgroup of G'. show the following:

a) a≈b iff φ(a)=φ(b), which defines an equivalence relation onG.

b) the inverse image φ-1(H) is a subgroup of G.

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Hubert Koch
Hubert KochLv2
31 Jan 2019

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