Abstract
Let F be a field of characteristic ≠2, D be a quaternion division algebra over F, and 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 D is algebraic over k. 2. Q ⊈ F. Let n be an integer, n ≥ 2. We study the completely reducible subgroups of GL n (D) that comprise a conjugate in GL n (D) of the group of all matrices diag(, 1,…, 1) ∈ GL n (D), a ∈ Q.
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