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Level and index in the modular group

Published online by Cambridge University Press:  14 November 2011

W. W. Stothers
W. W. Stothers
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Extract

It is shown that the index of a congruence subgroup of the modular group cannot be less than the level of the subgroup. This allows a number of existence theorems about non-congruence subgroups.

The level of a subgroup of the modular group can be defined in terms of the action on Q ∪ {∞}. We define a similar action to get information on congruence subgroups. In fact, we get a more powerful result, but this appears to be the most useful version.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 115 - 126
Copyright
Copyright © Royal Society of Edinburgh 1984

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