Let D be a division ring with center F, and let G be an almost subnormal subgroup of D*. In this paper, we show that ifGcontains a non-abelian locally solvable maximal subgroup, then D must be a cyclic algebra of prime degree over F. Moreover, it is proved that every locally nilpotent maximal subgroup of G is abelian. [ABSTRACT FROM AUTHOR]
In this paper, we introduce a strongly quasi-local version of the coarse Novikov conjecture, which states that a certain assembly map from the coarse Khomology of a metric space to the K-theory of its strongly quasi-local algebra is injective. We prove that the conjecture holds for metric spaces with bounded geometry which can be coarsely embedded into Banach spaces with Property (H), as introduced by Kasparov and Yu. We also generalize the notion of strong quasi-locality to proper metric spaces and provide a (strongly) quasi-local picture for K-homology. [ABSTRACT FROM AUTHOR]