Groups in which all subgroups of infinite special rank have bounded near defect. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Dixon, Martyn R.; Ferrara, Maria; Trombetti, Marco
• Is Part Of: Communications in algebra. Volume 46:Issue 12(2018)
• Page Start: 5416
• Page End: 5426
• Publication Date: 2018-12-02
• Subjects: Finite-by-nilpotent group -- finite special rank -- (n -- m)-subnormal subgroup; Primary -- 20E15 -- Secondary 20F19 -- 20F22; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1468908
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: If G is a group with subgroup H and n, m are two fixed non-negative integers, we say that H is ( n, m )-subnormal in G if there is a subgroup H 0 containing H such that| H 0 : H | ≤ n and H 0 is subnormal in G with subnormal defect at most m . We define S ( n, m ) to be the class of all groups of infinite special rank (and the trivial groups) whose subgroups of infinite special rank are ( n, m )-subnormal in G . In this paper, we show that S ( n, m )-groups are finite-by-nilpotent, in a large class of locally graded groups.