What's the sufficient or necessary conditions for a manifold to have Lie group structure? – mathoverflow.net

What's the sufficient or necessary conditions for a manifold to have Lie group structure? – mathoverflow.net

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For example, given a Lie group, its fundamental group must be Abelian. So $\Sigma_g$ ($g>1$) can't have Lie group structure. We also know for $S^n$ only $n=0,1,3$ can have Lie group structures. ...

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