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

Recall that a group is called semiabelian if it is generated by its normal cyclic subgroups [6]. The class of semiabelian groups is a very natural generalization of the wellknown class of Dedekind groups (the groups in which all cyclic subgroups are normal). In the paper [6] Venzke showed that these groups could play a major role in the theory of supersoluble finite groups. Based on the notion ...

In this paper, we give two descriptions of the languages recognized by finite supersoluble groups. We first show that such a language belongs to the Boolean algebra generated by the modular products of elementary commutative languages. An elementary commutative language is defined by a condition specifying the number of occurrences of each letter in its words, modulo some fixed integer. Our sec...

Abstract A classical result of Baer states that a finite group G which is the product two normal supersoluble subgroups if and only ʹ nilpotent. In this article, we show = AB (respectively, w -supersoluble) B , in permutes with every maximal subgroup each Sylow then -supersoluble), provided We also investigate products defined above when $ A\cap B=1 obtain more general results.