Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank) |
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| Authors: | Abdelhafid Badis Nadir Trabelsi |
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| Affiliation: | 1.Department of Mathematics, Faculty of Science,University of Tebessa,Tebessa,Algeria;2.Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics,University of Setif,Setif,Algeria |
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| 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. |
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