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

Badis, Abdelhafid; Trabelsi, Nadir

doi:10.2478/s11533-011-0077-0

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Cited by 2 publications

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“…Many results have been obtained on M N Xgroups, or more generally on groups whose proper subgroups are X-groups, for several choices of X. In particular in [2] (respectively, [5]), it is proved that a locally graded group whose proper subgroups are NC-groups (respectively, BC-groups) is itself an NC-group (respectively, BC-group). In other words, there are no locally graded M N NC-groups (respectively, M N BC-groups).…”

Section: Introductionmentioning

confidence: 99%

On Groups Whose Proper Subgroups Are Chernikov-by-Baer or (Periodic Divisible Abelian)-by-Baer

Arikan

Trabelsi

2013

J. Algebra Appl.

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Communicated by A. FacchiniIf X is a class of groups, then a group G is called a minimal non-X-group if it is not an X-group but all of its proper subgroups belong to X. In this paper we prove that locally graded minimal non-(Chernikov-by-nilpotent)-groups are precisely minimal non-nilpotent-groups without maximal subgroups and that locally graded minimal non-(Chernikov-by-Baer)-groups are locally finite and coincide with the normal closure of an element. We also prove that an infinite locally graded minimal non-((periodic divisible abelian)-by-Baer)-group G is an imperfect locally nilpotent p-group, for some prime p, and there is an element a in G such that G = a G .

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Section: Introductionmentioning

confidence: 99%