Group management : issue on creating new group with the name of an exsiting group on an other vertual site

As I understood actually the users are shared between all the site but not the groups, here the issue I noticed by playing a bit with this concept:
Created 2 users A , B on my site1,
Created a Group "common" on my site1 and added the my users A and B to it.
Created an other group with the same name "common" on an other site : site 2
Tried to add users to this group (on my site 2), in the user picker popup engine I have the list of the users of my site 1 containing users A , B...