On the set of grouplikes of a coring

We focus our attention to the set Gr(.) of grouplike elements of a coring . over a ring A. We do some observations on the actions of the groups U(A) and Aut(.) of units of A and of automorphisms of corings of ., respectively, on Gr(.), and on the subset Gal(.) of all Galois grouplike elements. Among them, we give conditions on . under which Gal(.) is a group, in such a way that there is an exact sequence of groups {1} . U(A g) . U(A) . Gal(.) . {1}, where A g is the subalgebra of coinvariants for some g . Gal(.)