This section contains much of the same principles of isomorphism as rings. There are a few ideas that are new for example: If *G* is abelian and *H* is nonabelian, then *G* and *H* are not isomorphic.Hungerford mentions this without a proof by explaining that if we were to form two tables (one for *G* and other for *H*) we would find that they are different and cannot be constructed in the same way and therefore they are not isomorphic. There must be a better explanation of why the above statement is true.

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