Translation of 'f agit sur C'

Question

In a French mathematical paper I am reading, there is the following situation: let $f,\sigma:A\rightarrow A$ two group homomorphisms and there is an $N$ such that $\ker (f)\subseteq C = \ker(\sigma^N -1)$. What does this mean in English: if we choose $N$ sufficiently large then we may assume that 'f agit sur C'?

Answer 1

"$f$ agit sur $C$" simply means the function $f$ maps the elements of $C$.

Depending on the context, this could sometimes mean that $C$ is then the domain of $f$.

However, as Jean-Marie pointed out, in this case, it probably doesn't mean that. We need more details to know this.