In this paper the authors study the class of locally graded groups all of whose subgroups are permutable or are soluble and satisfy a certain rank condition. The rank conditions in question include groups of finite abelian section rank, minimax groups and polycyclic groups. In each case necessary and sufficient conditions are given for a locally graded group to have all subgroups permutable or soluble with the given rank condition.
Groups with all subgroups permutable or soluble of finite rank / Dixon, M. R.; Ferrara, M.; Karatas, Z. Y.; Trombetti, M.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 549:(2020), pp. 195-214. [10.1016/j.jalgebra.2019.12.014]
Groups with all subgroups permutable or soluble of finite rank
Dixon M. R.;Trombetti M.
2020
Abstract
In this paper the authors study the class of locally graded groups all of whose subgroups are permutable or are soluble and satisfy a certain rank condition. The rank conditions in question include groups of finite abelian section rank, minimax groups and polycyclic groups. In each case necessary and sufficient conditions are given for a locally graded group to have all subgroups permutable or soluble with the given rank condition.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
