Centers

Let G be a connected Lie subgroup of \mathrm{GL}_n. Then A\in G commutes with all of G iff it commutes with all of \mathfrak{g}.

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Centers

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.

No Eckmann-Hilton