from the one described above. However, the Eckmann-Hilton argument shows that it does in fact agree with the above concatenation of loops, and moreover that the resulting group structure is abelian.

An inspection of the proof shows that, more generally, is abelian for any H-space , i.e., the multiplication need not have an inverse, nor does it have to be associative. For example, this shows that the fundamental group of a loop space