Irreducible linear groups of degree 3 over a quaternion division ring containing a root subgroup

摘要

We study the irreducible subgroups of GL(3)(D) over a quaternion division ring D of characteristic not equal2 that comprise a conjugate in GL(3)(D) of the group of all matricesdiag (((1)(0) (a)(1)),1), a is an element of k,where k is a central subfield of D such that D is algebraic over k.