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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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
Keywords
- Soluble groups
- Minimal non-Baer-groups
- Minimal non-nilpotent-groups
- Minimal non-(finite-by-Baer)-groups
- Minimal non-(finite-by-abelian)-groups