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In general how would one show that two groups are isomorphic?

I know that to show that they aren't you would try to show that some abstract property is not satisfied, such as they have different orders etc.

I can't see a straightforward way of showing that they are isomorphic though.

MHW
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  • Exhibit an isomorphism – Hagen von Eitzen Mar 09 '16 at 22:11
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    Well, generally speaking, this is not such an easy thing to do. However, in practice, one often writes down a bijective homomorphism between the two groups in question. Sometimes, there is an easy way to do this; sometimes not. The so-callled ''First Isomorphism Theorem'' for groups is often helpful in these situations. – Alex Wertheim Mar 09 '16 at 22:12

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