Groups with complete lattice of nearly normal subgroups.

Maria De Falco; Carmela Musella

Revista Matemática Complutense (2002)

  • Volume: 15, Issue: 2, page 343-350
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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De Falco, Maria, and Musella, Carmela. "Groups with complete lattice of nearly normal subgroups.." Revista Matemática Complutense 15.2 (2002): 343-350. <http://eudml.org/doc/44377>.

@article{DeFalco2002,
abstract = {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.},
author = {De Falco, Maria, Musella, Carmela},
journal = {Revista Matemática Complutense},
keywords = {Teoría de grupos; Subgrupos; Retículos; complete lattices; nearly normal subgroups; subgroups of finite index; lattices of subgroups; descending series of normal subgroups; ascending series of normal subgroups},
language = {eng},
number = {2},
pages = {343-350},
title = {Groups with complete lattice of nearly normal subgroups.},
url = {http://eudml.org/doc/44377},
volume = {15},
year = {2002},
}

TY - JOUR
AU - De Falco, Maria
AU - Musella, Carmela
TI - Groups with complete lattice of nearly normal subgroups.
JO - Revista Matemática Complutense
PY - 2002
VL - 15
IS - 2
SP - 343
EP - 350
AB - 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.
LA - eng
KW - Teoría de grupos; Subgrupos; Retículos; complete lattices; nearly normal subgroups; subgroups of finite index; lattices of subgroups; descending series of normal subgroups; ascending series of normal subgroups
UR - http://eudml.org/doc/44377
ER -

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