Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov

‎We pursue further our‎ ‎investigation‎, ‎begun in [H. Smith‎, ‎Groups with all subgroups subnormal or‎ ‎nilpotent-by-Chernikov‎, Rend‎. ‎Sem‎. ‎Mat‎. ‎Univ‎. ‎Padova, ‎۱۲۶ (۲۰۱۱)‎, ‎۲۴۵-۲۵۳] 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 $\mathfrak{X}$ 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.

Keywords:

locally finite groups , subnormal subgroups , nilpotent-by-Chernikov groups