= Orbit product of polynomial factors
{title2=$q_{\mathcal O}=\prod_{p\in\mathcal O}p$}
= Orbit products of polynomial factors
{synonym}
A <finite group> permutes the associate classes of irreducible <polynomial> factors of an invariant. The product of one representative from each orbit transforms by a scalar <character> of the group. If that <character> is trivial, the product is invariant. Its transitive factor orbit makes it prime in the invariant ring: an invariant <polynomial> divisible by one orbit factor is divisible by all of them.
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