15.97 (2002)

Let $p$ be a prime. A group $G$ satisfies the $p$-minimal condition if there are no infinite descending chains $G_1 > G_2 > \dots$ of subgroups of $G$ such that each difference $G_i \setminus G_{i+1}$ contains a $p$-element (S. N. Chernikov). Suppose that a locally finite group $G$ satisfies the $p$-minimal condition and has a subnormal series each of whose factors is finite or a $p'$-group. Is it true that all $p$-elements of $G$ generate a Chernikov subgroup?