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Keywords:
$\ell $-cyclically ordered set; completeness; monotone permutation; half cyclically ordered group
Summary:
For an $\ell $-cyclically ordered set $M$ with the $\ell $-cyclic order $C$ let $P(M)$ be the set of all monotone permutations on $M$. We define a ternary relation $\overline{C}$ on the set $P(M)$. Further, we define in a natural way a group operation (denoted by $\cdot $) on $P(M)$. We prove that if the $\ell $-cyclic order $C$ is complete and $\overline{C}\ne \emptyset $, then $(P(M), \cdot ,\overline{C})$ is a half cyclically ordered group.
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