Turkish Journal of Mathematics
DOI
-
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
First Page
165
Last Page
176
Recommended Citation
KURDACHENKO, LEONID ANDREEVICH and SMITH, HOWARD (2004) "Groups with Rank Restrictions on Non-Subnormal Subgroups," Turkish Journal of Mathematics: Vol. 28: No. 2, Article 7. Available at: https://journals.tubitak.gov.tr/math/vol28/iss2/7
