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 126 (2011), 245{253] and continued in [g. cutolo and h. smith, locally _nite 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 _nite p-groups in the class x, where p is a prime, while an earlier article provided a reasonable classi- _cation 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 .