Trying to translate the paper "COHOMOLOGIE ET GROUPE DE STEINBERG RELATIFS" by J P Loday J Alg (54) 178, 1978

Question

I am trying to translate the paper "COHOMOLOGIE ET GROUPE DE STEINBERG RELATIFS" by J P Loday J Alg (54) 178, 1978 using google traslator. In section 1, he writes

Un morphisme d’extensions relatives de $(Q, N)$, soit $(\alpha): (M, \mu) \rightarrow (M’, \mu’)$, est la donnee d’un homomorphisme de groupes $N$-equivariant $\alpha:M \rightarrow M'$ tel que $\mu' \alpha=\mu$. Remarquons que $\alpha$ definit par restriction un homomorphisme de $Q$-modules $L \rightarrow L'$ entre les noyaux.

Une congruence d’extenrions relatives de $(Q, N)$ par le $Q$-module $L$ est un morphisme d’extensions relatives qui induit l’identite sur les noyaux. L’ensemble des classes de congruences d’extensions relatives de $(Q, N)$ par le $Q$-module $L$ est note $Ext(Q, N; L)$.

Using the google I found following:

A morphism of relative extensions $(Q, N)$, say $(\alpha):(M,\mu) \rightarrow(M',\mu')$ is an $N$-equivariant group homomorphism $\alpha:M \rightarrow M'$ such that $\mu' \alpha=\mu$. Note that $\alpha$ defines a $Q$-module homomorphism between the core .

A congruence of relative extenrions $(Q, N)$ by the $Q$-module $L$ is a morphism of extensions on which induces identity on the cores. The set of congruence classes of extensions on $(Q, N)$ by the $Q$-module $L$ is denoted $Ext(Q, N, L)$.

I do not understand what this "noyaux" mean. In both the paragraph it translates "core" or "nuclei"

Answer 1

Noyau means kernel, as in the kernel of a morphism of groups.