Massey Exercise 2.3.2
Suppose that for any two points , all path classes from to induce the same isomorphism . From the last exercise, we see that any two paths in the space (between any points because and are arbitrary), must have the property that is in the center of . But, any loop in can be considered as the product of a path to some other point and its inverse. So, every member of is in the center. That is, the fundamental group of must be abelian.