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Tagged with group-cohomology group-rings
3 questions
13
votes
1
answer
548
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Generators for the first cohomology of free groups
Let $F = \langle x_1, \dots, x_n \rangle$ be the free group on $n$ generators and $R = \mathbb Z$. The Fox derivatives $\frac{\partial}{\partial x_i} \colon F \to R[F]$ are the unique derivations ...
8
votes
1
answer
538
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Abstract proof that $\lvert H^2(G,A)\rvert$ counts group extensions
(This question is originally from Math.SE, where it didn't receive any answers.)
$\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\ext}{...
7
votes
2
answers
485
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Using Dunwoody's results on cohomological dimension to learn about a von Neumann regular group ring
Just recently I've stumbled across Warren Dicks' book Groups, trees and projective modules (1980) and I was pretty stunned. I know nothing of group cohomology, but I gather the "tree" ...