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Let $A_{5}$ be the alternating subgroup of the symmetric group $S_{5}$. Prove that $A_{5}$ is generated by the two elements $\{a=(123),b=(12345)\}$, or equivalently can we write the element $(234)$ as a composition of the two elements $a$ and $b$.

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    This is a virtual duplicate of another recent question. What have you tried?2012-04-16
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    I would also be interested in how you know that the two alternatives are equivalent.2012-04-16
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    The group is usually called "Alternating group", not "alternative."2012-04-16

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