On Nonmodular Periodic Finitary Linear Groups

Very recently M. S. Lucido proved that for any prime p, a periodic finitary linear p′-group G of characteristic p is isomorphic to some finitary linear group G0 of characteristic zero. Moreover G0 can be chosen to be irreducible whenever G is irreducible. Here we offer an alternative proof, one that is somewhat shorter, more explicit and more elementary. We then generalize this result by proving that the same conclusion holds for periodic finitary skew linear p′-groups of characteristic p; that is, we replace fields by division rings in the hypotheses. This is less elementary.