Groups with Rank Restrictions on Non-Subnormal Subgroups

Authors : Leonid A. KURDACHENKO

Pages : 165-176

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let G be a group in which every non-subnormal subgroup has finite rank. This paper considers the question as to which extra conditions on such a group G ensure that G has all subgroups subnormal. For example, if G is torsion-free and locally soluble-by-finite then either G has finite 0-rank or G is nilpotent. Several results are obtained on soluble insert ignore into journalissuearticles values(respectively, locally soluble-by-finite); groups satisfying the stated hypothesis on subgroups.
Keywords : Subnormal subgroups, locally soluble by finite groups, finite Mal`cev rank