No Eckmann-Hilton

Prove the following two statements and conclude that the fundamental group of a (connected) topological group G is abelian:

1) A discrete normal subgroup of a connected topological group is central.
2) If p:\hat{G}\to G is the universal covering, the total space \hat{G} admits a topological group structure such that p is a group morphism. The kernel of p is then isomorphic to the fundamental group of G.

Advertisements
No Eckmann-Hilton