Locally nilpotent skew linear groups

Abstract

Throughout this paper D denotes a division ring with centre F and n a positive integer. A subgroup G of GL( n ,D) is absolutely irreducible if the F -subalgebra F[G] enerated by G is the full matrix ring D n × n . It is completely reducible (resp. irreducible ) if row n -space D n over D is completely reducible (resp. irreducible), as D–G bimodule in the obvious way. Absolutely irreducible skew linear groups have a more restricted structure than irreducible skew linear groups, see for example [ 7 ],[ 8 ], [8] and [10]. Here we make a start on elucidating the structure of locally nilpotent suchgroups.