Order n-transitivity
= Order n-transitivity
An ordered <permutation group> is order n-transitive if it can send any increasing $n$-tuple to any other increasing $n$-tuple. This compares tuples with the same relative order, unlike unrestricted <n-transitive group actions>. In the usual transitive chain setting, order two-transitivity implies every finite order-transitivity for a <lattice-ordered permutation group>.