- Turkish Journal of Mathematics
- Vol: 28 Issue: 2
- Groups with Rank Restrictions on Non-Subnormal Subgroups
Groups with Rank Restrictions on Non-Subnormal Subgroups
Authors : Leonid A. Kurdachenko
Pages : 165-176
View : 10 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
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