= Absolute residue degree
{title2=$f_{\mathfrak q}=[\mathcal O_F/\mathfrak q:\mathbb F_p]$}
The absolute <residue degree> is the degree of the <residue field> over its prime field. For a tower above $p$, degrees multiply: $[k_{\mathfrak q}:\mathbb F_p]=[k_{\mathfrak q}:k_{\mathfrak p}][k_{\mathfrak p}:\mathbb F_p]$. In a <Galois extension> over $\mathbb Q$, the <decomposition group> has a cyclic <quotient group> of this order by its <inertia group>. This can exclude <residue degrees> even when the whole extension has that degree: $S_3$ has no cyclic <quotient group> of order six.
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