Soluble minimal non-(finite-by-Baer)-groups |
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Authors: | Abdelhafid Badis Nadir Trabelsi |
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Institution: | 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: | Let
\mathfrakX{\mathfrak{X}} be a class of groups. A group G is called a minimal non-
\mathfrakX{\mathfrak{X}}-group if it is not an
\mathfrakX{\mathfrak{X}}-group but all of whose proper subgroups are
\mathfrakX{\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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Keywords: | |
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