Groups with Rank Restrictions on Non-Subnormal Subgroups

Authors: LEONID ANDREEVICH KURDACHENKO, HOWARD SMITH

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 (respectively, locally soluble-by-finite) groups satisfying the stated hypothesis on subgroups.

Keywords: Subnormal subgroups; locally soluble-by-finite groups; finite Mal'cev rank

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