if G is free group of rank >1 , Show that the commutator [G,G] has infinite rank. Please help, I tried to find an expression of the commutator but I have no idea
commutator of free group has infinite rank
2
$\begingroup$
abstract-algebra
group-theory
free-groups
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1Relevant: http://math.stackexchange.com/questions/983480/commutator-subgroup-of-rank-2-free-group-is-not-finitely-generated In particular read the answer by Timbuc and the comment below it – 2017-02-19
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0need for any rank grater than one , not only for rank =2 – 2017-02-20
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0Well...if you have it for rank two then you have if for **any** rank bigger than two ....right? – 2017-02-20