On Hankel operators associated with linearly ordered abelian groups

We consider two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups. Criteria for the boundedness and compactness of these operators are given, in particular, in terms of functions of bounded mean oscillation. It is proved that the generalized Hankel operators are non-Fredholm. Some applications to the theory of Toeplitz operators on groups are given.