On ‘Clifford’s Theorem’ for primitive finitary groups

Wehrfritz, B.

doi:10.1090/S0002-9939-97-04038-0

On ‘Clifford’s Theorem’ for primitive finitary groups
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by B. A. F. Wehrfritz PDF

Proc. Amer. Math. Soc. 125 (1997), 2843-2846 Request permission

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

U. Meierfrankenfeld, Ascending subgroups of irreducible finitary linear group, J. London Math. Soc. (2) 51 (1995), no. 1, 75–92. MR 1310723, DOI 10.1112/jlms/51.1.75
G. A. Miller, H. F. Blichfeldt, and L. E. Dickson, Theory and applications of finite groups, Dover Publications, Inc., New York, 1961. MR 0123600
Peter M. Neumann, The lawlessness of groups of finitary permutations, Arch. Math. (Basel) 26 (1975), no. 6, 561–566. MR 412280, DOI 10.1007/BF01229781
B. A. F. Wehrfritz, Primitive finitary skew linear groups, Arch. Math. (Basel) 62 (1994), no. 5, 393–400. MR 1274743, DOI 10.1007/BF01196427
B. A. F. Wehrfritz, Locally soluble primitive finitary skew linear groups, Comm. Algebra 23 (1995), no. 3, 803–817. MR 1316733, DOI 10.1080/00927879508825250