Group A - Grant admin permissions - Server and Database level permissions
Group B - Grant Select / Execute - Database level permissions.
Using database mapping for the group only needing Select and Execute to specific databases.
You may want to do some reading so you gain a better understand the different levels of permissions.
http://msdn.microsoft.com/en-us/library/ms188659(v=sql.105).aspx
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AJ Mendo | @SQLAJ