1-dependent theories better known as NIP theories are the first class of the hierarchy of n-dependent structures. The random n-hypergraph is the canonical object which is n-dependent but not (n-1)-dependent. Thus the hierarchy is strict. Recently, in a joint work with Chernikov, we proved the existence of strictly n-dependent groups for all natural numbers n and we started studying their properties. The connected component over A, inspired by the definition of the connected component of algebraic group, is the intersection of all A-type definable subgroups of bounded index. A crucial fact about (type)definable groups in 1-dependent theories is the absoluteness of their connected components: Namely given a definable group G and a small set of parameters A, we have that the connected component of G over A coincides with the one over the empty set. A
 
We will give examples of n-dependent groups and discuss a generalization of absoluteness of the connected component to n-dependent theories.