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Soluble-by-periodic skew linear groups

Published online by Cambridge University Press:  24 October 2008

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
Queen Mary College, London El 4NS
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Let D be a division ring with central subfield F, n a positive integer and G a subgroup of GL(n, D) such that the F-subalgebra F[G] generated by G is the full matrix algebra Dn×n. If G is soluble then Snider [9] proves that G is abelian by locally finite. He also shows that this locally finite image of G can be any locally finite group. Of course not every abelian by locally finite group is soluble. This suggests that Snider's conclusion should apply to some wider class of groups.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 379 - 389
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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