So I've been presented with the following:
Let F be a field, G a finite group and N a normal subgroup of G. Let I be the 2 sided ideal I of the group algebra FG generated by {n-1 | n $\in$ N, n $\neq$ 1}. Show that the factor algebra FG/I is isomorphic to the group algebra F(G/N) of the factor group G/N.
As far as I can tell, all I need to do is create the map
$f: \frac{FG}{I} \rightarrow F(\frac{G}{N})$ s.t. $f(g+I) = gN$.
From here the three conditions for an algebra isomorphism work out easily. Forgive me if this is obvious, but why do I need I generated by {n-1 | n $\in$ N, n $\neq$ 1}?
Because in both algebras, elements of $N$ are identified with $1$, and identifying $n$ with $1$ is equivalent to identifying $n-1$ with $0$.