The varieties of the mod p cohomology rings of extra special p-groups for an odd prime p

Abstract

In this paper we attempt to determine the mod p cohomology rings of the extra special p-groups for an odd prime p. Quillen has calculated the mod 2 case [8]. In our case, its structure seems to be very complicated [6]. It seems reasonable that we consider the variety defined by the cohomology ring of even degree according to Serre [11]. The main result of this paper (Theorem 5.3) gives a subalgebra of the cohomology ring such that the inclusion homomorphism induces a homeomorphism between the varieties.