[Richard-B]

Just had to do this on an installation, here is the code:

function bp_group_remove_tabs() {
	global $bp;
	if (isset($bp->groups->current_group->slug) && $bp->groups->current_group->slug == $bp->current_item) 
	{
	// Duplicate the line below changing 'home' for each tab you wish to remove	 
         $bp->bp_options_nav[$bp->groups->current_group->slug]['home'] = false;		 		 
	}
}
add_action( 'bp_setup_nav', 'bp_group_remove_tabs', 999 );