A note on groups with many locally supersoluble subgroups

Document Type : Ischia Group Theory 2014


Dipartimento di Matematica e Applicazioni - University of Napoli Federico II


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 Cernikov 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 group whose non-(locally supersoluble) subgroups lie into finitely many conjugacy classes must be locally supersoluble.


Main Subjects

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Volume 4, Issue 2 - Serial Number 2
Proceedings of the Ischia Group Theory 2014-Part II.
June 2015
Pages 1-7
  • Receive Date: 14 March 2015
  • Revise Date: 17 April 2015
  • Accept Date: 17 April 2015
  • Published Online: 01 June 2015