= Annihilator of a subgroup of a finite abelian group
{title2=$K^\perp$}
For a <subgroup> $K$ of a <finite abelian group> $G$, its annihilator is
$$
K^\perp=\{\chi\in\widehat G:\chi(k)=1\text{ for every }k\in K\}.
$$
These are exactly the <linear characters> that descend to the <quotient group> $G/K$. The <character group of a finite abelian group> has the same size as the group, so $|K^\perp|=|G/K|=|G|/|K|$. The annihilator is what <abelian hidden-subgroup Fourier sampling> measures.
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