Rank-Engel conditions on linear groups.

We study linear groups G for which for every g in G there exists a subgroup E of G satisfying some sort of rank condition and such that for every x in G there is a positive integer m such that for all n ≥ m the repeated commutator [x, _ng] lies in E. If E can always be chosen to be a Chernikov group (resp. a polycyclic-by-finite group) such G can be completely described (Wehrfritz in Adv Group Theory Appl 7:143–157, 2019; Wehrfritz in Boll Unione Mat Ital, to appear). For more general rank conditions our analyses below are complete for positive characteristics but are less so for characteristic zero. [ABSTRACT FROM AUTHOR]