Rings of invariants of certain p-groups over the field F-p

We use Nakajima's (J. Algebra 85 (1983), 253-286) characterization of p-gro ups with polynomial rings of invariants over the field Fp to prove that max imal proper subgroups of such groups have rings of invariants that are hype rsurfaces. We give an explicit construction for the ring of invariants of s uch a group, as a module over the ring of invariants of the total group. (C ) 1999 Academic Press.