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The classical modular group as a subgroup of GL(2, ℤ)†

Published online by Cambridge University Press:  18 May 2009

Morris Newman
Morris Newman
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106, U.S.A.
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The title is somewhat misleading, since the classical modular group Г= PSL(2, ℤ) is certainly not a subgroup of GL(2, ℤ). What is meant of course are the faithful representations of F as a subgroup of GL(2, ℤ), where Г is to be thought of as the free product of a cyclic group of order 2 and a cyclic group of order 3. No such representation is possible as a subgroup of SL(2, ℤ); it is necessary to have matrices of determinant −1 as well.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 161 - 164
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Newman, M., Some free products of cyclic groups, Michigan Math. J. 9 (1962), 369–373.CrossRefGoogle Scholar
2.Newman, M., Integral Matrices (Academic Press, 1972).Google Scholar