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 be an infinite-dimensional vector space over any division ring , and let be an irreducible primitive subgroup of the finitary group . We prove that every non-identity ascendant subgroup of is also irreducible and primitive. For a field, this was proved earlier by U. Meierfrankenfeld.

**1.**U. Meierfrankenfeld,*Ascending subgroups of irreducible finitary linear group*, J. London Math. Soc. (2)**51**(1995), no. 1, 75–92. MR**1310723**, 10.1112/jlms/51.1.75**2.**G. A. Miller, H. F. Blichfeldt, and L. E. Dickson,*Theory and applications of finite groups*, Dover Publications, Inc., New York, 1961. MR**0123600****3.**Peter M. Neumann,*The lawlessness of groups of finitary permutations*, Arch. Math. (Basel)**26**(1975), no. 6, 561–566. MR**0412280****4.**B. A. F. Wehrfritz,*Primitive finitary skew linear groups*, Arch. Math. (Basel)**62**(1994), no. 5, 393–400. MR**1274743**, 10.1007/BF01196427**5.**B. A. F. Wehrfritz,*Locally soluble primitive finitary skew linear groups*, Comm. Algebra**23**(1995), no. 3, 803–817. MR**1316733**, 10.1080/00927879508825250

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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

Received by editor(s):
April 25, 1996

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1997
American Mathematical Society