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

Abstract

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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.

How to cite

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Abdelhafid 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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  7. [7] Kleidman P.B., Wilson R.A., A characterization of some locally finite simple groups of Lie type, Arch. Math. (Basel), 1987, 48(1), 10–14 Zbl0595.20027
  8. [8] Napolitani F., Pegoraro E., On groups with nilpotent by Černikov proper subgroups, Arch. Math. (Basel), 1997, 69(2), 89–94 Zbl0897.20021
  9. [9] Newman M.F., Wiegold J., Groups with many nilpotent subgroups, Arch. Math. (Basel), 1964, 15, 241–250 Zbl0134.26102
  10. [10] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups. I, Ergeb. Math. Grenzgeb., 62, Springer, Berlin-Heidelberg-New York, 1972 
  11. [11] Smith H., More countably recognizable classes of groups, J. Pure Appl. Algebra, 2009, 213(7), 1320–1324 http://dx.doi.org/10.1016/j.jpaa.2008.11.030 Zbl1172.20029
  12. [12] Wehrfritz B.A.F., Infinite Linear Groups, Ergeb. Math. Grenzgeb., 76, Springer, Berlin-Heidelberg-New York, 1973 

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