By Sylow Theorem, all Sylow p-subgroups of $A_5$ are conjugate, for any $p\in \{ 2,3,5\}$.
But why all subgroups of Alternating group A5 of order 2 are conjugate?
2026-03-25 01:18:18.1774401498
Why all subgroups of order 2 of Alternating group A5 are conjugate?
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Hint: The elements of order $2$ in $S_n$ are the products of disjoint transpositions. What are the elements of order $2$ in $A_5$?