Some completely reducible linear groups over a quaternion division ring containing a root subgroup
by
Evgenii Bashkirov
Belorussian State University of Informatics and Radioelectronics, Minsk

Let F be a field of characteristic different from 2, D a quaternion division algebra over F. Let Q be a subgroup of the additive group of D which satisfies the following two conditions: (1)Q contains a subfield k of F such that F is algebraic over k; (2)Q contains an element which does not belong to F. Let n be an integer not less then 2. By t₁₂(a) we denote a matrix of degree n whose diagonal entries are 1, the 12-position is a and zeros are everywhere else. We study the completely reducible subgroups of the group G=GL_n(D) that comprise a conjugate in G of the group of all matrices t₁₂(a) in G where a runs over k.

References.

E. L. Bashkirov. Some completely reducible linear groups over a quaternion division ring containing a root subgroup. Comm. Algebra 31(2003), 5727-5754.

Date received: March 24, 2004