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I was told that the fundamental group of a connected, compact, semisimple Lie group is finite, with the outline of a possible way to prove this fact. Is there any source however that fleshes this out in detail / are there several ways to prove this fact?

Thanks!

(OK: this The result is often known as Weyl's theorem, and I found a source in Knapp--the proof seems very different from think for his take on the outline I was presented....proof, Knapp provides a fairly detailed exposition of his perspective.)
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I was told that the fundamental group of a connected, compact, semisimple Lie group is finite, with the outline of a possible way to prove this fact. Is there any source however that fleshes this out in detail / are there several ways to prove this fact?

Thanks!

(OK: this is known as Weyl's theorem, and I found a source in Knapp--the proof seems very different from the outline I was presented....)
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I was told that the fundamental group of a connected, compact, semisimple Lie group has a is finitefundamental group, with the outline of a possible way to prove this fact. Is there any source however that fleshes this out in detail / are there several ways to prove this fact?

Thanks!
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