To find an inverse of k-cycle for example $(1,2,4,6,3)$ we write it from right to left $(3,6,4,2,1)$ but is it the right or left inverse? as $S_n$ is not abelian for $n\leq 3$
2026-03-25 04:39:29.1774413569
Finding An Inverse Of K-Cycle
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$$(12463)(36421)=(1)(2)(3)(4)(5)(6)=I$$ $$(36421)(12463)=(1)(2)(3)(4)(5)(6)=I$$ These are the same and it is a right and left inverse. Note that if a group is not Abelian, it does not mean that $a\not=b\ \forall\ a,b\in S$. It just means that $a=b\ \forall\ a,b\in S$ is not true for some $a,b\in S$.