# The nilpotency of some groups with all subgroups subnormal.

Leonid A. Kurdachenko; Howard Smith

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 2, page 411-421
- ISSN: 0214-1493

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topKurdachenko, Leonid A., and Smith, Howard. "The nilpotency of some groups with all subgroups subnormal.." Publicacions Matemàtiques 42.2 (1998): 411-421. <http://eudml.org/doc/41347>.

@article{Kurdachenko1998,

abstract = {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.},

author = {Kurdachenko, Leonid A., Smith, Howard},

journal = {Publicacions Matemàtiques},

keywords = {Grupo nilpotente; Criterio minimax; Familias de subgrupos; Clausura normal; subnormal subgroups; minimax groups; nilpotency},

language = {eng},

number = {2},

pages = {411-421},

title = {The nilpotency of some groups with all subgroups subnormal.},

url = {http://eudml.org/doc/41347},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Kurdachenko, Leonid A.

AU - Smith, Howard

TI - The nilpotency of some groups with all subgroups subnormal.

JO - Publicacions Matemàtiques

PY - 1998

VL - 42

IS - 2

SP - 411

EP - 421

AB - 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.

LA - eng

KW - Grupo nilpotente; Criterio minimax; Familias de subgrupos; Clausura normal; subnormal subgroups; minimax groups; nilpotency

UR - http://eudml.org/doc/41347

ER -

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