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Soluble minimal non-(finite-by-Baer)-groups

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Abstract

Let \({\mathfrak{X}}\) be a class of groups. A group G is called a minimal non-\({\mathfrak{X}}\)-group if it is not an \({\mathfrak{X}}\)-group but all of whose proper subgroups are \({\mathfrak{X}}\)-groups. In [16], Xu proved that if G is a soluble minimal non-Baer-group, then G/G ′′ is a minimal non-nilpotent-group which possesses a maximal subgroup. In the present note, we prove that if G is a soluble minimal non-(finite-by-Baer)-group, then for all integer n ≥ 2, G/γ n (G′) is a minimal non-(finite-by-abelian)-group.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Tebessa, 12000, Tebessa, Algeria

    Abdelhafid Badis

  2. Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, University of Setif, 19000, Setif, Algeria

    Nadir Trabelsi

Authors
  1. Abdelhafid Badis
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  2. Nadir Trabelsi
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Correspondence to Abdelhafid Badis.

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Communicated by F. de Giovanni.

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Badis, A., Trabelsi, N. Soluble minimal non-(finite-by-Baer)-groups. Ricerche mat. 59, 129–135 (2010). https://doi.org/10.1007/s11587-009-0070-0

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  • DOI: https://doi.org/10.1007/s11587-009-0070-0

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