Full paper in PDF:
$%M. de Falco and C. Musella, Groups with complete lattice of nearly normal subgroups,
Rev. Mat. Complut. 15 (2002), no. 2, 343–350.%$
ABSTRACT
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.