Complex sentence: It is not a resolvent invariant for, as being invariant by, in fact, it is a resolvent invariant for the dihedral subgroup, and is used to define the resolvent cubic of the quartic equation.
Split into simpler sentences: It is not a resolvent invariant for, as being invariant by. In fact, it is a resolvent invariant for the dihedral subgroup, and is used to define the resolvent cubic of the quartic equation.