On monotone permutations of`ℓ-cyclically ordered sets
Ján Jakubík · Czechoslovak Mathematical Journal · 2006
For an ℓ-cyclically ordered set M with the ℓ-cyclic order C let P(M) be the set of all monotone permutations on M. We define a ternary relation $$\bar C$$ on the set P(M). Further, we define in a natural way a group operation (denoted by ·) on P(M). We prove that if the ℓ-cyclic order C is complete and $$\bar C$$ ≠ 0, then (P(M),·, $$\bar C$$ ) is a half cyclically ordered group.