The Brauer-Long group of [formula omitted]/ p t[formula omitted]-dimodule algebras

Abstract

Let G be a cyclic group of prime power order p t , and R a connected commutative ring containing 1/ p and ‘enough’ roots of unity. We compute the Brauer–Long group, BD( R, G) by showing that BD( R, G) is isomorphic to the set of 5-tuples Z/2 Z × Aut(G) × Gal(R, GR) × Gal(R, RG) × B(R) with a suitable multiplication defined on this set.