Hypercentrality and hypercyclicity in skew linear groups (Q1080528)

In the paper, we are concerned with skew linear groups G over division rings D, of characteristic \(p\geq 0\), that are locally finite-dimensional over some subfield E, where E is not necessarily central in D. Our main result is to show that locally nilpotent such groups are not necessarily hypercentral (and so locally supersoluble such groups need not be hypercyclic). However, we show that if G is as above such that the maximal unipotent normal subgroup u(G) is trivial or \(p=0\), then G is locally nilpotent if and only if G is hypercentral, but there exists a locally supersoluble such group G that is not hypercyclic.