Clifford theory with Schur indices (Q1340448)

A concept of central simple \(G\)-algebras is introduced, as well as an equivalence relation among central simple \(G\)-algebras. From it, a set of equivalence classes is obtained which generalizes the Brauer group of a field, as well as the Brauer-Wall group. It is shown that the elements of this set are the natural objects that control the Clifford theory with Schur indices for a finite group \(H\) with a normal subgroup \(N\) with \(G\simeq H/N\).