This paper is devoted to the study of groups $G$ in the universe $c\bar{\mathfrak L}$ of all radical locally finite groups with min-$p$ for all primes $p$ such that every $\delta$-chief factor of $G$ is either a cyclic group of prime order or a quasicyclic group. We show that within the universe $c\bar{\mathfrak L}$ this class of groups behaves very much as the class of finite supersoluble groups.
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