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Subnormality conditions in non-torsion groups

Published online by Cambridge University Press:  17 April 2009

Luise-Charlotte Kappe  and
Gunnar Traustason
Luise-Charlotte Kappe
Affiliation:
SUNY at Binghamton, Binghamton, NY 13902-6000, United States of America e-mail: menger@math.binghamton.edu
Gunnar Traustason
Affiliation:
University of BathBath BA2 7AY, England e-mail: masgt@maths.bath.ac.uk
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Abstract

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According to results of Heineken and Stadelmann, a non-torsion group is a 2-Baer group if and only if it is 2-Engel, and it has all subgroups 2-subnormal if and only if it is nilpotent of class 2. We extend some of these results to values of n greater than 2. Any non-torsion group which is an n-Baer group is an n-Engel group. The converse holds for n = 3, and for all n in the case of metabelian groups. A non-torsion group without involutions having all subgroups 3-subnormal has nilpotency class 4, and this bound is sharp.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 459 - 465
Copyright
Copyright © Australian Mathematical Society 1999

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