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 $b$.
generators of alternating groups?
1
$\begingroup$
symmetric-groups
-
0This is a virtual duplicate of another recent question. What have you tried? – 2012-04-16
-
1I would also be interested in how you know that the two alternatives are equivalent. – 2012-04-16
-
2The group is usually called "Alternating group", not "alternative." – 2012-04-16