Groups with the weak minimal condition for non-subnormal subgroups |
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Authors: | Leonid A Kurdachenko Howard Smith |
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Institution: | (1) Present address: Department of Mathematics, University of Dnepropetrovsk, Ukraine;(2) Present address: Department of Mathematics, Bucknell University, 17837 Lewisburg, PA, USA |
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Abstract: | Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main results are as follows. If G is locally nilpotent then either G is minimax or G has all subgroups subnormal; if G is a Baer group then all subgroups of G are subnormal. It is also proved that a generalised radical group with this property is soluble-by-finite and either is minimax or has all subgroups subnormal. |
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