The maximality of monomial subgroups of linear groups over division rings (Q1825284)

The author proves that the full monomial group is a maximal subgroup of GL(n,D), where D is a division ring and \(n\geq 2\) an integer, except for those cases that are already exceptions when D is commutative (these are fully listed). The author then considers the corresponding problem for SL(n,D). This too he settles, except that if D is infinite, commutative and of characteristic not 2 he needs to assume that D has enough squares. The proofs look elementary, but the calculations are fierce.