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...

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.

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 ...

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.

We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima’s fixed point free C∞ action on S of the affine group of the line cannot be approximated by analytic actions. An example is given of an analytic, fixed point free action on S of a solvable group that is not supersoluble.

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.