Let $a$ and $b$ be two non-disjoint cycles of order $m$ and $n$. Is there any general formula for the order of $a b$? I understand that we can convert any non-disjoint cycles into disjoint cycles and compute the order as the lcm of the orders of individual cycles. I am looking for a formula which takes information about $a$ and $b$ as input.
2026-04-02 20:11:03.1775160663
Order of product of non-disjoint cycles
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As has been noted in the comments, there is no such formula. The order of $ab$ depends on the common elements and their positions in the two cycles.