LOCALLY FINITE p-GROUPS WITH ALL SUBGROUPS EITHER SUBNORMAL OR NILPOTENT-BY-CHERNIKOV

Abstract. We pursue further our investigation, begun in [H. Smith, Groups with all subgroups subnormal or nilpotent-by-Chernikov, Rend. Sem. Mat. Univ. Padova 126 (2011), 245{253] and continued in [G. Cutolo and H. Smith, Locally finite groups with all subgroups subnormal or nilpotent-by- Chernikov. Centr. Eur. J. Math. (to appear)] of groups G in which all subgroups are either subnormal or nilpotent-by-Chernikov. Denoting by X the class of all such groups, our concern here is with locally finite p-groups in the class X, where p is a prime, while an earlier article provided a reasonable classi- fication of locally nite X-groups in which all of the p-sections are nilpotent-by-Chernikov. Our main result is that if G is a Baer p-group in X then G is nilpotent-by-Chernikov .