The name for a subobject(subgroup) which is annihilated by action I know this question is easy, but for the life of me, I cannot remember what we call this thing. Googling for this has offered no help.
Consider an object $A$ and a second object $B$(let them be groups if you so choose). We wish to consider and action of $A$ on $B$. Moreover there is a subobject $C \hookrightarrow B$(subgroup) which is annihilated by the action of $A$, i.e. the restriction of the action of $A$ on $B$ to $C$ sends $C$ to the zero object(the zero in $B$ which corresponds to the trivial group).
I thought it would be the kernel of the action, but this term is reserved for something else(in particular those objects which fix everything).
I think that this should be referred to as Torsion, and in particular, in the back of my mind, I keep thinking it is called the $A$-Torsion of $B$. But I am not sure.
Does anyone know what this has been called in the past?

in linear algebra, the subspace annihilated by a linear mapping $A$ is the nullity of $A$.
