Rings of Invariants of Certainp-Groups over the FieldFp

We use Nakajimaʹs (J. Algebra85(1983), 253–286) characterization ofp-groups with polynomial rings of invariants over the fieldFpto prove that maximal proper subgroups of such groups have rings of invariants that are hypersurfaces. We give an explicit construction for the ring of invariants of such a group, as a module over the ring of invariants of the total group.