gistfile1.txt

GroupOneController = RouteController.extend({
  activeTab: 'groupOne',
  // ...
});

PageController = GroupOneController.extend({
  // inherits 'activeTab'
  // ...
});

UI.registerHelper('activeTab', function(name) {
  if (Router.current() && Router.current().activeTab === name)
    return 'active';
});

<button class="{{activeTab 'groupOne'}}">Group One</button>