It seems this solved the issue:
$('#content-main').load(pageName + " .fragment");
Thou', don't know why the other method did not work...
I have to add, since the DIV with class ".fragment" will be loaded into DIV #content-main, one has to beware to not create nested DIVs. I solved the problem because I have a DIV below #content-main on each html, where I will put the class .fragment.