An Introduction to Abstract Algebra (Vol II) by F.M. Hall

a2. Example 5. As in the first example of 4 above, where H is the group of even integers under addition. Example 6. Let G be the cyclic group of order 3, generator a, and let H be the symmetric group of degree 4. Consider the mapping 0 which sends 1234 e into (1 2 3 4)' 1234 a into (2 3 1 4) 1234 and a2 into (3 1 2 4) It may easily be verified that 0 is a homomorphism. The idea of homomorphism is an extremely important one. It gives us a method of linking two groups together, so that we may learn more about the properties of one by knowing those of the other.

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