How to find number of homomorphisms between z8 and s4? I check by taking image of generator of z8 Say f:z8---->s4 O(f(1))/8 O(f(1))=1,2,4 S4 has 15 elements of order 2 and 6 elements of order 4 15+6+1(trivial)=22 Is this correct?
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I only count 9 elements of order 2: Six with a single 2-cycle and three with two disjoint 2-cycles. Am I missing something? Regardless of which one of us is counting correctly, the rest of the proof looks good to me. – Arthur Nov 15 '18 at 09:02
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Arthur, your answer is correct. – Radhika Jain Nov 23 '18 at 17:51