The Complete Reducibility of Locally Completely Reducible Finitary Linear Groups |
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Authors: | Wehrfritz B A F |
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Institution: | School of Mathematical Sciences, Queen Mary and Westfield College Mile End Road, London E1 4NS |
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Abstract: | Let V be a vector space over some division ring D, and G a finitarysubgroup of GL(V). If G is locally completely reducible, thenthe D-G modules V, V, G] and V/CV(G) need not be completelyreducible, even if dimDV is finite. Moreover, if F is a field,then V and V/CV(G) need not be completely reducible. We provehere that if D is a finite-dimensional division algebra andG is locally completely reducible, then V, G] is always a completelyreducible D-G module. 1991 Mathematics Subject Classification20H25. |
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