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Proceedings of the American Mathematical Society

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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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B. A. F. Wehrfritz
Affiliation: School of Mathematical Sciences, Queen Mary & Westfield College, Mile End Road, London E1 4NS, England

Received by editor(s): April 25, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society