The recognition principle [Boardmann–Vogt, May] states that a grouplike algebra over the little $n$-disks/cube operad is weakly equivalent to an $n$-fold loop space. There are technical hypotheses though: in May's version for example, the space has to be compactly generated, weakly Hausdorff, and have a non-degenerate base point.
The grouplike condition is clearly necessary. This might be well-known to experts, but is there an easy example of a grouplike $E_n$-algebra which is not weakly equivalent to an $n$-fold loop space (therefore not satisfying one of the other, technical hypotheses)?
