Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.
@article{urn:eudml:doc:41347,
title = {The nilpotency of some groups with all subgroups subnormal.},
journal = {Publicacions Matem\`atiques},
volume = {42},
year = {1998},
pages = {411-421},
mrnumber = {MR1676035},
zbl = {0921.20033},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41347}
}
Kurdachenko, Leonid A.; Smith, Howard. The nilpotency of some groups with all subgroups subnormal.. Publicacions Matemàtiques, Tome 42 (1998) pp. 411-421. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41347/