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'?
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4"(the function) $f$ acts on $C$" – Mauro ALLEGRANZA May 26 '17 at 13:47
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...the verb being "agir" – Jean Marie May 26 '17 at 13:55
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So the group $A$ is abelian? – Hagen von Eitzen May 27 '17 at 12:10
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Yes, it is an abelian variety, could that be relevant to the translation? – Lhavinia May 27 '17 at 12:12
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Maybe not, but it is certainly relevant in order to speak of $\ker(\sigma^N-1)$ – Hagen von Eitzen May 27 '17 at 12:13
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"$f$ 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.
Stephen
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I am sorry but I think it's more than that: it is the action of a group on a set... but we have not enough elements to be sure of that. – Jean Marie May 26 '17 at 13:57
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