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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?

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    @BBischof, the thing is, what you generalized into is difficult to make sense of (in a general category, there is no sense in which an object can act on another, and "annihilation" does not make sense in a general category, either; &c.) . If you want a more general question, I think it would be optimal to state in detail the situation you *do* know of, and ask for what is a more general situation extending yours.2010-10-09

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

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    @Mariano: "Nullity" is used, but for the *dimension* of the kernel. "Nullspace", however, is *very* common (e.g., it occurs in Friedberg/Insel/Spence's book).2010-10-09