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Normal subgroups of skew linear groups

Published online by Cambridge University Press:  26 February 2010

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
Department of Mathematics, Queen Mary College, London, El 4NS
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Extract

In a series of papers we have analysed the embedding of certain groups H as normal subgroups of absolutely irreducible skew linear groups G, see [7], [8], [9] and [10]. Here we drop the absolutely irreducibility assumption on G. If H is locally finite we derive relatively strong conditions on G, although not as strong as when G is absolutely irreducible. If H is abelian, very much in contrast to the absolutely irreducible case, we show that nothing can be said. The phrase “bounded by an integer-valued function of n only” we abbreviate to “n-bounded”.

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Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 102 - 110
Copyright
Copyright © University College London 1986

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References

1.Amitsur, S. A.. Finite subgroups of division rings. Trans. Amer. Math. Soc., 80 (1955), 361–386.CrossRefGoogle Scholar
2.Cohn, P. M.. Algebra II (John Wiley & Sons, New York, 1977).Google Scholar
3.Kegel, O. H. & F, B. A. F.. Locally Finite Groups (North Holland, Amsterdam, 1973).Google Scholar
4.Wehrfritz, B. A. F.. Infinite Linear Groups (Springer, Berlin, 1973).CrossRefGoogle Scholar
5.Wehrfritz, B. A. F.. Complete reducibility in skew linear groups. J. London Math. Soc. (2), 28 (1983), 301–309.CrossRefGoogle Scholar
6.Wehrfritz, B. A. F.. Faithful representations of finitely generated abelian by polycyclic groups over division rings. Quart. J. Math. (2), 35 (1984), 361–372.CrossRefGoogle Scholar
7.Wehrfritz, B. A. F.. Locally finite normal subgroups of absolutely irreducible skew linear groups. J. London Math. Soc. (2), 32 (1985), 88–102.CrossRefGoogle Scholar
8.Wehrfritz, B. A. F.. On absolutely irreducible skew linear groups in characteristic zero. Arch. Math. (Basel)., 45 (1985), 193–199.CrossRefGoogle Scholar
9.Wehrfritz, B. A. F.. Soluble normal subgroups of skew linear groups. J. Pure and Appl. Algebra. To appear.Google Scholar
10.Wehrfritz, B. A. F.. Locally nilpotent skew linear groups. Proc. Edinburgh Math. Soc., 29 (1986), 101–113.CrossRefGoogle Scholar
11.ZalesskiĪ, A. E.. The Structure of several classes of matrix groups over a division ring (Russian). Sibirsk. Mat. Ž. 8 (1967), 1284–1298. = Siberian Math. J., 8 (1967), 978–988.Google Scholar