Full paper in PDF:
$%M. de Falco and C. Musella, Groups with complete lattice of nearly normal subgroups,
Rev. Mat. Complut. 15 (2002), no. 2, 343–350.%$
Groups with Complete Lattice of Nearly
Normal Subgroups
Maria DE FALCO and Carmela MUSELLA
Dipartimento di Matematica e Applicazioni
Università degli studi di Napoli Federico II
Complesso Universitario di Monte S. Angelo
Via Cintia
I 80126, Napoli — Italy
Received: May 21, 2001
Revised: December 13, 2001
A subgroup
of a group
is said to be nearly normal in
if it has finite
index in its normal closure in
. A well-known theorem of B. H. Neumann
states that every subgroup of a group
is nearly normal if and only if
the commutator subgroup
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.
2000 Mathematics Subject Classification: 20E15, 20F24.