I'm sure a lot of you are in the same boat as me.. where you'll log in after a day or so away and see a gazillion notifications from groups that you have joined - about things for sale or events going on, some of which you're too late on and missed entirely because you didn't log into SL in time to see the notification.
So.. I'd like to suggest that we have the option to select whether or not we'd like to receive offline notifications from groups so that we aren't missing out on things happening in SL. Make it one of the options that you can select (or turn off) in the group's General tab.