Abstract

For any pair of division rings k and F with K ⊃ F and dim F K = r we determine all the overgroups of SL( n, K) in GL( nr, F), as well as the overgroups of Sp( n, K) in GL( nr, F) (for commutative K and even n). The overgroups of SU( n, K, f) and Ω(n, K, Q) in GL(nr, F) will be determined in another paper, “Overgroups in GL( nr, F) of certain subgroups of SL( n, K), II”.

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