# Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)

Abdelhafid Badis; Nadir Trabelsi

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1344-1348
- ISSN: 2391-5455

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topAbdelhafid Badis, and Nadir Trabelsi. "Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)." Open Mathematics 9.6 (2011): 1344-1348. <http://eudml.org/doc/269633>.

@article{AbdelhafidBadis2011,

abstract = {Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.},

author = {Abdelhafid Badis, Nadir Trabelsi},

journal = {Open Mathematics},

keywords = {Locally graded; Locally (soluble-by-finite); Baer; Chernikov; Finite rank; locally graded groups; Baer groups; Baer-by-Chernikov groups; finitely generated subgroups; subgroups of finite index; subnormal subgroups},

language = {eng},

number = {6},

pages = {1344-1348},

title = {Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)},

url = {http://eudml.org/doc/269633},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Abdelhafid Badis

AU - Nadir Trabelsi

TI - Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1344

EP - 1348

AB - Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.

LA - eng

KW - Locally graded; Locally (soluble-by-finite); Baer; Chernikov; Finite rank; locally graded groups; Baer groups; Baer-by-Chernikov groups; finitely generated subgroups; subgroups of finite index; subnormal subgroups

UR - http://eudml.org/doc/269633

ER -

## References

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