Currently displaying 1 – 8 of 8

Showing per page

Order by Relevance | Title | Year of publication

On almost normal subgroups of supersoluble groups

Carmela Musella — 1999

Bollettino dell'Unione Matematica Italiana

Un sottogruppo H di un gruppo G si dice «almost normal» se ha soltanto un numero finito di coniugati in G , e ovviamente l'insieme a n G costituito dai sottogruppi almost normal di G è un sottoreticolo del reticolo L G di tutti i sottogruppi di G . In questo articolo vengono studiati gli isomorfismi tra reticoli di sottogruppi almost normal, provando in particolare che se G è un gruppo supersolubile e G ¯ è un gruppo FC-risolubile tale che i reticoli a n G e a n G ¯ sono isomorfi, allora anche G ¯ è supersolubile, e...

Groups with nearly modular subgroup lattice

Francesco de GiovanniCarmela Musella — 2001

Colloquium Mathematicae

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...

Some lattice properties of normal-by-finite subgroups

Maria De FalcoCarmela Musella — 2003

Bollettino dell'Unione Matematica Italiana

A subgroup H of a group G is said to be normal-by-finite if the core H G of H in G has finite index in H . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then G is abelian-by-finite, provided that all its periodic homomorphic images are locally finite. The aim of this article is to describe the structure of groups G for which the partially ordered set nf G consisting of all normal-by-finite subgroups satisfies certain relevant...

Groups with complete lattice of nearly normal subgroups.

Maria De FalcoCarmela Musella — 2002

Revista Matemática Complutense

A subgroup H of a group G is said to be nearly normal in G if it has finite index in its normal closure in G. A well-known theorem of B.H. Neumann states that every subgroup of a group G is nearly normal if and only if the commutator subgroup G' is finite. In this article, groups in which the intersection and the join of each system of nearly normal subgroups are likewise nearly normal are considered, and some sufficient conditions for such groups to be finite-by-abelian are given.

Groups with Normality Conditions for Non-Periodic Subgroups

Maria De FalcoFrancesco de GiovanniCarmela Musella — 2011

Bollettino dell'Unione Matematica Italiana

The structure of (non-periodic) groups in which all non-periodic subgroups have a prescribed property is investigated. Among other choices, we consider properties generalizing normality, like subnormality, permutability and pronormality. Moreover, non-periodic groups whose proper non-periodic subgroups belong to a given group class are studied.

Page 1

Download Results (CSV)