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Why do highly composite rows on the bad Laver tables have longer periods?

For all natural numbers $n$, let $(B_{n},*_{n})$ be the algebraic structure with underlying set $\{1,\dots,n\}$ where $x*_{n}1=x+1\mod n$, $n*_{n}y=y$, and $x*_{n}(y+1)=(x*_{n}y)*_{n}(x+1)$ for $x<...
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