Homomorphisms and subgroups
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Solution Summary
This shows how to give examples of a non-trivial group homomorphism, a basis for a given homomorphism, and 2-Sylow subgroups (or explain why none exists).
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(a) This non-trivial group homomorphism does not exist.
Proof: Suppose is a non-trivial group homomorphism. We consider an element in . We know is the set of all even permutations and each permutation can be expression as the multiplication of disjoint cycles. So can only be the ...
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