Subgroups of bounded residue in ultraproducts of finite groups

We consider a variety of linearity generalizations: finitary linearizability, local linearizability, and so on. The natural partial ordering on the set of classes of generalized linear groups under examination is described in full. Criteria for abstract groups to be finitary linearized in terms of ultraproducts of linear and finite groups are proven. Examples of nilpotent groups are given which have not faithful finitary linear representations by automorphisms of vector spaces over a field. © 1997 Plenum Publishing Corporation.