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Algebra: Abstract and Modern by U. M. Swamy, A. V. S. N. Murthy

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5

Homomorphisms of Groups

Homomorphisms play a major role in all aspects of modern algebra. One of the most difficult problems in the theory of groups is to list all finite groups having the same order. The difficulty is that we may list the same groups in different forms. The notion of isomorphism builds up an equivalence relation between groups, so that we may consider two groups belonging to a given equivalence class as the same. Just as we cannot conclude that two human beings are same, because they wear an identical set of clothes or the same person putting on a different set of clothes does not become different, groups are to ...

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