SQL Server - Windows Group Authentication
You were correct in creating the Windows domain security group.  Add Windows domain accounts to that security group as required.  You were correct in creating a SQL login for the Windows domain group.  SQL will allow authentication by any member of that Windows domain group.  Nothing further is required as far as SQL login creation.  Set permissions as needed within SQL Server.  

Have you tested your configuration?  What problems are you encountering?


  By using Windows Authentication, Windows groups can be created at the domain level, and a login can be created on SQL Server for the entire group. Managing access from at the domain level can simplify account administration.


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