ON A CLASS OF SUPERSOLUBLE GROUPS

A Class of Generalized Supersoluble Groups

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.

Supersoluble Groups

We shall term a group G supersoluble if every homomorphic image H9*l of G contains a cyclic normal subgroup different from 1. Supersoluble groups with maximum condition, in particular finite supersoluble groups, have been investigated by various authors: Hirsch, Ore, Zappa and more recently Huppert and Wielandt. In the present note we want to establish the close connection between supersoluble ...

Languages Recognized by Finite Supersoluble Groups

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...

a note on groups with many locally supersoluble subgroups

it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

A Class of Two Generated Automaton Groups on a Three Letter Alphabet