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Solvable-by-finite subgroups of GL(2, F)

Published online by Cambridge University Press:  18 May 2009

Abdul Majeed  and
A. W. Mason
Abdul Majeed
Affiliation:
University of the Punjab (Lahore)
A. W. Mason
Affiliation:
University of Glasgow
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In a recent paper [5] Tits proves that a linear group over a field of characteristic zero is either solvable-by-finite or else contains a non-cyclic free subgroup. In this note we determine all the infinite irreducible solvable-by-finite subgroups of GL(2, F), where F is an algebraically closed field of characteristic zero. (Every reducible subgroup of GL(2, F) is metabelian.) In addition, we prove that an irreducible subgroup of GL(2, F) has an irreducible solvable-by-finite subgroup if and only if it contains an element of zero trace.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 1 , January 1978 , pp. 45 - 48
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

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