  Orthogonality in model theory captures the idea of absence of non-trivial
interactions between definable sets. We introduce a somewhat opposite notion of
cohesiveness, capturing the idea of interaction among all parts of a given
definable set. A cohesive set is indecomposable, in the sense that if it is
internal to the product of two orthogonal sets, then it is internal to one of
the two. We prove that a definable group in an o-minimal structure is a product
of cohesive orthogonal subsets. If the group has dimension one, or it is
definably simple, then it is itself cohesive. Finally, we show that an abelian
group definable in the disjoint union of finitely many o-minimal structures is
a quotient, by a discrete normal subgroup, of a direct product of locally
definable groups in the single structures.
