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Let G be a group with identity eG and let H be a group

Chapter 8, Problem 3E

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QUESTION:

Let G be a group with identity \(e_G\) and let H be a group with identity \(e_H\). Prove that G is isomorphic to \(G \oplus \{e_H\}\) and that H is isomorphic to \(\{e_G\} \oplus H\).

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QUESTION:

Let G be a group with identity \(e_G\) and let H be a group with identity \(e_H\). Prove that G is isomorphic to \(G \oplus \{e_H\}\) and that H is isomorphic to \(\{e_G\} \oplus H\).

ANSWER:

Step 1 of 4

Given that  and  groups with identity elements  and  respectively. To prove and .

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