a1 School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS
Throughout this paper p denotes an odd prime. The groups we shall consider are central extensions of a cyclic subgroup by Cp Cp, and may be presented as
The group P(n) is defined for each n ≥ 3, and has order pn. The group P(3) is the non-abelian group of order p3 and exponent p. The mod-p cohomology rings of the other groups of order p3 have been known for some time (see  or  for that of the non-abelian metacyclic group), and so this paper completes the calculation of the mod-p cohomology rings of the groups of order p3.
(Received July 05 1991)
(Revised November 18 1991)