Are the braid groups $\mathcal{B}_n$ virtually abelian ? virtually free ?
Subgroups of the braid groups $\mathcal{B}_n$
4
$\begingroup$
group-theory
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1See http://math.stackexchange.com/questions/48780/mathcalb-3-modulo-the-normal-closure-of-mathbbz-times-mathbbz/48950#48950 for virtual abelianness when $n=3$. – 2011-07-23
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1Braid groups are torsion free, so they can't be virtually free (or they would be free themselves). They can't be virtually abelian because then they would have to be nilpotent (but they contain free subgroups). – 2011-07-23
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0But free groups are virtually free! – 2011-07-23