Weak Engel Conditions on Linear Groups

Abstract

We study several weak Engel conditions on linear groups, starting from the “almost Engel” condition of Khukhro and Shumyatsky. There the groups were Engel modulo certain finite subsets. Here we replace “finite subsets” by “Chernikov subgroups” in one case and “polycyclic-by-finite subgroups” in another. We also include a shorter proof of a theorem of Shumyatsky characterizing linear almost Engel groups.

Keywords

• Engel condition
• linear group
• matrix group