Cohomology ring of the finite split metacyclic group

Abstract

Let G be the finite split metacyclic group of presentation G=<A, B | A^m=Bⁿ=e, BAB^-1= A^r, rⁿ ≡ 1(m), (n(r-1), m)=1>. Huebschmann computed the integral cohomology ring of a large class of metacyclic groups using the mechanism of homological perturbation theory and determined the generators of the subring of even degree classes of any metacyclic group by means of the Chern classes of some of its representations. The purpose of this article is to investigate H^∗(G; ℤ) by localization methods. It also aims to determine explicit representations of G whose Chern classes generate H^∗(G; ℤ) by induction techniques.