Essential cohomology and extraspecial $p$-groups

Pham Anh Minh
2000 Transactions of the American Mathematical Society  
Let p be an odd prime number and let G be an extraspecial pgroup. The purpose of the paper is to show that G has no non-zero essential mod-p cohomology (and in fact that H * (G, Fp) is Cohen-Macaulay) if and only if |G| = 27 and exp(G) = 3. Let us recall that an extraspecial p-group G is of order p 2n+1 (n ∈ N) and is isomorphic to one of the following central products of groups: are extraspecial p-groups of order p 3 . Note that These groups can be obtained cohomologically as follows. Let V be
more » ... s follows. Let V be a vector space of dimension 2n + 1 over the prime field F p with basis e, a 1 , .
doi:10.1090/s0002-9947-00-02689-1 fatcat:6iuhcdrgjrbzzfzr2o6zrvoy4a