Duality for almost completely decomposable groups

AbstractWe establish a duality for near-isomorphism categories of almost completely decomposable groups through a combination of Butler duality and Warfield duality. We are then able to dualize results in the literature to obtain classifications and structure theories for new classes of almost completely decomposable groups. For example, known results on p-local crq-groups, those groups X that contain a completely decomposable subgroup B with X/B a cyclic p-group, can be dualized to results on p-local co-crq groups, those groups Y that embed in a completely decomposable group B so that the quotient B/Y is a cyclic p-group. A variety of other applications is given