Linear Groups of Degree 4 Over a Quaternion Division Ring that Contain the Special Unitary Group of a Skew-Hermitian Form with Maximal Witt Index

Abstract

The paper describes subgroups of the general linear group GL 4(D) over a quaternion division ring D that contain the special unitary group of degree 4 over a non-central subfield of D. The connections between these subgroups and the spinor groups of appropriate symmetric bilinear forms are established.