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

• Autorzy: Abdelhafid Badis , Nadir Trabelsi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Locally graded; Locally (soluble-by-finite); Baer; Chernikov; Finite rank

Kategorie tematyczne

• 20E07: Subgroup theorems; subgroup growth
• 20F19: Generalizations of solvable and nilpotent groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1344-1348

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Abdelhafid Badis

• University of Tebessa

autor

Nadir Trabelsi

• University of Setif

Bibliografia

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• [8] Napolitani F., Pegoraro E., On groups with nilpotent by Černikov proper subgroups, Arch. Math. (Basel), 1997, 69(2), 89–94
• [9] Newman M.F., Wiegold J., Groups with many nilpotent subgroups, Arch. Math. (Basel), 1964, 15, 241–250
• [10] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups. I, Ergeb. Math. Grenzgeb., 62, Springer, Berlin-Heidelberg-New York, 1972
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Identyfikatory

DOI

10.2478/s11533-011-0077-0