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Notice that we did not prove that H itself is abelian—only the image. This foreshadows the concept of a homomorphic image preserving certain properties but not all.

Paolo Aluffi's Algebra: Chapter 0 takes a category-theoretic approach that some find more elegant but others find too abstract for a first exposure. One reviewer noted that Aluffi's book is "perhaps too abstract for a first read (though it's also in some sense cleaner / more focused due to the abstraction)". Pinter avoids these abstractions entirely, focusing instead on concrete examples and careful exposition. a book of abstract algebra pinter solutions better