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