A family of finitep‐groups satisfying Carlson's depth conjecture

Abstract

AbstractLet be a prime number and letrbe an integer with . For eachr, let moreover denote the unique quotient of the maximal class pro‐pgroup of size . We show that the mod‐pcohomology ring of has depth one and that, in turn, it satisfies the equalities in Carlson's depth conjecture [2]. This is the first family of finitep‐groups for which Carlson's depth conjecture has been verified besidesp‐groups of abelian type mod‐pcohomology or extraspecialp‐groups. Moreover, this computation is possible without first describing the structure of the cohomology ring.