Groups in which all subgroups of infinite special rank have bounded near defect. Issue 12 (2nd December 2018) - Dixon, Martyn R.; Ferrara, Maria; Trombetti, Marco
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.