Two-cocycle
= Two-cocycle
For a $G$-module $M$, a two-cocycle is a map $c:G\times G\to M$ satisfying
$$
g\cdot c(h,k)-c(gh,k)+c(g,hk)-c(g,h)=0.
$$
= Two-cocycle
For a $G$-module $M$, a two-cocycle is a map $c:G\times G\to M$ satisfying
$$
g\cdot c(h,k)-c(gh,k)+c(g,hk)-c(g,h)=0.
$$