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Question Number 11372 by agni5 last updated on 22/Mar/17

$$\mathrm{If}{\mathrm{G}}_1\mathrm{and}{\mathrm{G}}_2\mathrm{are}\mathrm{groups},\mathrm{and}\mathrm{f}:{\mathrm{G}}_1\to {\mathrm{G}}_2$$$$\mathrm{is}\mathrm{a}\mathrm{group}\mathrm{homomorphism},\mathrm{then}\mathrm{prove}$$$$\mathrm{that}\mathrm{o}\left({\mathrm{G}}_1\right)=\mathrm{o}\left({\mathrm{G}}_2\right).$$

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