Groups generated by involutions, numberings of posets, and central measures

We define a new class of countable groups, which are defined by its action on the set monotonic numberings (diagrams) an arbitrary finite or partial ordered (poset). These groups generated involutions? and in case posets could be considered as generalization Coxeter's symmetric groups. discuss problems concerned to infinite jf this type, particular problem descripton invariant measures space (central measures)with respect actions those The probelms tightly connected with theory representations generalizations group.