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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On `Clifford's theorem'
for primitive finitary groups


Author: B. A. F. Wehrfritz
Journal: Proc. Amer. Math. Soc. 125 (1997), 2843-2846
MSC (1991): Primary 20H25
MathSciNet review: 1415375
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Abstract: Let $V$ be an infinite-dimensional vector space over any division ring $D$, and let $G$ be an irreducible primitive subgroup of the finitary group $\mathrm {FGL} (V)$. We prove that every non-identity ascendant subgroup of $G$ is also irreducible and primitive. For $D$ a field, this was proved earlier by U. Meierfrankenfeld.


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Additional Information

B. A. F. Wehrfritz
Affiliation: School of Mathematical Sciences, Queen Mary & Westfield College, Mile End Road, London E1 4NS, England
Email: b.a.f.wehrfritz@qmw.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04038-0
PII: S 0002-9939(97)04038-0
Received by editor(s): April 25, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society