Active Directory Security Groups

I’m trying to add a Security Group for Active Directory in Windows 2003. When I try to add the security group under security permissions for a directory, I still cannot access the directory, but when I add the single users to the permissions, I can. I was wondering if it’s possible that the security group object is corrupt or am I not doing something right? I add the group under Domain\Users. The Group Scope is Global and the group type is Distribution.