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.
@article{urn:eudml:doc:44377,
title = {Groups with complete lattice of nearly normal subgroups.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {15},
year = {2002},
pages = {343-350},
zbl = {1021.20018},
mrnumber = {MR1951815},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44377}
}
De Falco, Maria; Musella, Carmela. Groups with complete lattice of nearly normal subgroups.. Revista Matemática de la Universidad Complutense de Madrid, Tome 15 (2002) pp. 343-350. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44377/