The paraheight of certain skew linear groups (Q1076157)

In the paper, the paraheights of hypercyclic subgroups G of GL(n,D), where D is a division ring that is locally finite-dimensional over its centre, are considered. The main result is that for any positive integer n and cardinal number c, there exists a division ring D, which is locally finite-dimensional over its centre, and a hypercyclic subgroup G of GL(n,D) such that G has paraheight w if c is finite and \(w+1\) if c is infinite, where w is the least ordinal of cardinality c. The results differ markedly from those for linear groups, where the paraheight of any hypercyclic linear group is bounded by a function of n.