Hi everybody. Which would be the best option in this case? Adding the nofollow tag to the facebook button or not? I am not sure. Thanks very much.
If you are linking you your own fanpage then why to make it nofollow? Google do not penalize for such kind of links.
There is no difference, because if you link to another Facebook page, it's not a problem. Also, if you link to your OWN page (where you have also a backlink to your homepage), the link from Facebook is nofollow, so I would keep the link TO Facebook dofollow!
If it actually leads to your Facebook page, then it's not a problem. If it doesn't, then be prepared for Google's retribution - it hates doorway pages and unscrupulous links. There's no need to add the nofollow tag.
My advice is to put nofollow on that kind of link, you will transfer the link juice to something that doesn't have effect. In 95% cases, a facebook page doesn't need organic search authority. It's social, not organic.