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On `Clifford's theorem' for primitive finitary groups

Author(s): B. A. F. Wehrfritz
Journal: Proc. Amer. Math. Soc. 125 (1997), 2843-2846.
MSC (1991): Primary 20H25
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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.

References:

1.: U. Meierfrankenfeld, Ascending subgroups of irreducible finitary linear group, J. London Math. Soc. 51 (1995), 75-92. MR 96c:20092
2.: G. A. Miller, H. F. Blichfeldt and L. E. Dickson, Theory and applications of finite groups, Dover Reprint, New York, 1961. MR 23:A925
3.: P. M. Neumann, The lawlessness of groups of finitary permutations, Arch. Math. 26 (1975), 561-566. MR 54:406
4.: B. A. F. Wehrfritz, Primitive finitary skew linear groups, Arch. Math. 62 (1994), 393-400. MR 95i:20071
5.: -, Locally soluble primitive finitary skew linear groups, Communications in Algebra 23 (1995), 803-817. MR 96a:20070


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