Consider the kernel of the homomorphism from two copies of the free group $F_2 \times F_2$ onto the integers sending every generator to 1. How to see that this subgroup is not finitely presented?
Non finitely presented subgroup
8
$\begingroup$
group-theory
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0Sorry, what's $F_2$? Surely not the field of two elements? – 2011-04-28
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2Surely the free group of rank 2. – 2011-04-28
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1This looks related: http://mathoverflow.net/questions/54975/when-is-a-finitely-generated-group-finitely-presented/54982#54982 – 2011-04-28
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0Ah, I mis-parsed it. It's not, "two copies of (the free group $F_2\times F_2$)," it's that $F_2\times F_2$ is two copies of the free group $F_2$. So, what are the generators of $F_2\times F_2$? – 2011-04-28