Gtalk is a free IM & VOIP service from Google. In this we can set our current status as available, busy and some custom status. If we want to be in invisible(Looks like Offline for your group members), we must log-in to Gail, Orkut or iGoogle. But it is somewhat difficult for Users with low bandwidth(low speed internet) to open chat in Gmail Orku or in iGoogle pages. The only way for those kind of connections is using Gtalk. But in the normal version of Gtalk , it is impossible to be in invisible mode.
But it is possible with the Labs Edition of Gtalk. But in this case the labs edition doesn't connect with very slow connection(connects in very rare cases). (If you want to download, Gtalk Labs Edition, use the Link1.) So we can leave this option.
The Nice idea behind my post is using the Multiple IM client Pidgin. First of all download this application using the Link2(below this post). Then Add your Gtalk IM with Pidgin as shown in the image below.
Then click on the down arrow nearer to your status. Then click on New status and type the TitleOffline and select invisible from Status. And finally click on Save and use. That's all. Now you can be in invisible mode even in slow connections.