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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

9 votes

How many non-isomorphic extensions with kernel $S^1$ and quotient cyclic of order $p$?

There is a short exact sequence of coefficients $\mathbb{Z}\rightarrow \mathbb{R}\rightarrow \mathbb{R}/\mathbb{Z}=S^1$. This gives you a long exact sequence of cohomology groups. For a finite group …
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