I know I should not change the core, but I do not know how to do otherwise.
By changing the core, I can remove the ‘public groups’ among those available during the creation process of the group.
In truth, to remove the radio button, I do not modify the core but a view of the active theme.
But the default groups are still created as public. This occurs when you create the group by setting only the name and description of the group (first step).