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, <em>Rend‎. ‎Sem‎. ‎Mat‎. ‎Univ‎.</em> <em>‎Padova,</em> ‎<strong>126</strong> (2011)‎, ‎245-253] and continued in [G. Cutolo and H. Smith‎, ‎Locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-Chernikov‎. ‎<em>Centr‎. ‎Eur‎. ‎J‎. ‎Math.,</em> (to appear)] ‎‎‎of groups $G$ in which all subgroups are either subnormal or‎ ‎nilpotent-by-Chernikov‎. ‎Denoting by $mathfrak{X}$ the class of all such‎ ‎groups‎, ‎our concern here is with locally finite p-groups in the class‎ ‎$mathfrak{X}$‎, ‎where $p$ is a prime‎, ‎while an earlier article provided a‎ ‎reasonable classification of locally finite $mathfrak{X}$ nb-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 $mathfrak{X}$ then $G$ is nilpotent-by-Chernikov‎.