We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.
@article{bwmeta1.element.doi-10_2478_s11533-009-0012-9,
author = {Leonid Kurdachenko and Howard Smith},
title = {Groups with small deviation for non-subnormal subgroups},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {186-199},
zbl = {1195.20032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0012-9}
}
Leonid Kurdachenko; Howard Smith. Groups with small deviation for non-subnormal subgroups. Open Mathematics, Tome 7 (2009) pp. 186-199. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0012-9/
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