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Possible Duplicate:
Homomorphism between $A_5$ and $A_6$

Why is it true that every element of the image of the function $f: A_5\longrightarrow A_6$ (alternating groups) defined by $f(x)=(123)(456) x (654)(321)$ does not leave any element of $\{1,2,3,4,5,6\}$ fixed (except the identity)?

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    @anon the digit 6 is not allowed to occur in $x$.2012-10-15
  • 0
    oops! ${}{}{}{}$2012-10-15

2 Answers 2