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THE COMPLETE REDUCIBILITY OF LOCALLY COMPLETELY REDUCIBLE FINITARY LINEAR GROUPS

Published online by Cambridge University Press:  01 March 1997

B. A. F. WEHRFRITZ
B. A. F. WEHRFRITZ
Affiliation:
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 finitary subgroup of GL(V). If G is locally completely reducible, then the D-G modules V, [V, G] and V/CV(G) need not be completely reducible, even if dimDV is finite. Moreover, if F is a field, then V and V/CV(G) need not be completely reducible. We prove here that if D is a finite-dimensional division algebra and G is locally completely reducible, then [V, G] is always a completely reducible D-G module.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 173 - 176
Copyright
© The London Mathematical Society 1997

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