# Groups with every subgroup ascendant-by-finite

Open Mathematics (2013)

- Volume: 11, Issue: 12, page 2182-2185
- ISSN: 2391-5455

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topSergio Camp-Mora. "Groups with every subgroup ascendant-by-finite." Open Mathematics 11.12 (2013): 2182-2185. <http://eudml.org/doc/269049>.

@article{SergioCamp2013,

abstract = {A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.},

author = {Sergio Camp-Mora},

journal = {Open Mathematics},

keywords = {Ascendant subgroup; Locally nilpotent; Radical; Locally finite group; locally finite groups; subgroups of finite index; ascendant subgroups; permutable subgroups; locally nilpotent subgroups},

language = {eng},

number = {12},

pages = {2182-2185},

title = {Groups with every subgroup ascendant-by-finite},

url = {http://eudml.org/doc/269049},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Sergio Camp-Mora

TI - Groups with every subgroup ascendant-by-finite

JO - Open Mathematics

PY - 2013

VL - 11

IS - 12

SP - 2182

EP - 2185

AB - A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

LA - eng

KW - Ascendant subgroup; Locally nilpotent; Radical; Locally finite group; locally finite groups; subgroups of finite index; ascendant subgroups; permutable subgroups; locally nilpotent subgroups

UR - http://eudml.org/doc/269049

ER -

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