Nonabelian first cohomology
= Nonabelian first cohomology
{title2=$H^1(G,B)$}
For a group $G$ acting by automorphisms on a possibly noncommutative group $B$, $H^1(G,B)$ is the pointed set of maps satisfying $c_{\sigma\tau}=c_\sigma\sigma(c_\tau)$ modulo $c_\sigma\mapsto b c_\sigma\sigma(b)^{-1}$. It classifies twisting of a reference action. It need not be an abelian group.