Groups with nearly modular subgroup lattice

• Autorzy: Francesco de Giovanni , Carmela Musella
• Języki publikacji: EN

Abstrakty

EN

A subgroup H of a group G is nearly normal if it has finite index in its normal closure $H^{G}$. A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we study the structure of groups in which all subgroups are nearly modular, proving in particular that a locally graded group with this property has locally finite commutator subgroup.

Kategorie tematyczne

• 20F24: FC-groups and their generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 88
• Numer: 1
• Strony: 13-20

Daty

wydano

2001

Twórcy

autor

Francesco de Giovanni

• Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy

autor

Carmela Musella

• Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy

Identyfikatory

DOI

10.4064/cm88-1-2