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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?

  • 0
    Sorry, what's $F_2$? Surely not the field of two elements?2011-04-28
  • 2
    Surely the free group of rank 2.2011-04-28
  • 1
    This looks related: http://mathoverflow.net/questions/54975/when-is-a-finitely-generated-group-finitely-presented/54982#549822011-04-28
  • 0
    Ah, 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

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