# Cohomological dimension of groups & number of generators

I have a torsion-free non-abelian nilpotent group $\Gamma$ of cohomological dimension $n$. Is it possible to say anything about the number of generators of $\Gamma$ in a minimal presentation?

Can I assume that the number of generators can be chosen to be less than $n$?

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Think about surface groups... –  Steve D Apr 16 '13 at 3:28
...or about nonabelian free groups... –  Misha Apr 16 '13 at 3:36
Since the question has been answered in comments I have voted to close as no longer relevant. –  Benjamin Steinberg Apr 16 '13 at 3:38
An alternative would be to make a community wiki answer that quotes Steve D and Misha's answers, and have that accepted. –  Ryan Budney Apr 16 '13 at 5:42
It seems, with the edit adding the word "nilpotent", that this became a reasonable question, so closing is perhaps unnecessary now. –  Lee Mosher Apr 17 '13 at 15:11