I´m adding facebook like buttons to my wordpress-page. On single.php, for every blog publish - which works fine. However I would like to include facebook like button towards the posts around the index page. I possibly could do this, however the url retrieved may be the primary index page, making sense. It is possible to way I'm able to have multiple like buttons on my small blog primary page, but still make every one of these to indicate the publish?

Yes, you place the href parameter for everybody like button towards the publish permalink. It is the data-href attribute within the HTML version:

<div class="fb-like" data-href="http://example.com/your-blog-post" data-send="true" data-width="450" data-show-faces="true"></div>

Well, within the index page and inside "The Loop", you could utilize the the_permalink() work as your Like button href.