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Francesco Polizzi
Francesco Polizzi
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By the modular group I either mean either $SL(2,\mathbb{Z})$, or $PSL(2,\mathbb{Z})$.

Where can I find examples of these?

Another question -: is there a good (ideally analytical, but possibly computer-aided) way to determine if a subgroup of the modular group generated by some given matrices ishas finite index? (and then, and possibly allowing to compute the index?)

  • will

By the modular group I either mean $SL(2,\mathbb{Z})$, or $PSL(2,\mathbb{Z})$.

Where can I find examples of these?

Another question - is there a good (ideally analytical, but possibly computer-aided) way to determine if a subgroup of the modular group generated by some given matrices is finite index? (and then to compute the index?)

  • will

By the modular group I mean either $SL(2,\mathbb{Z})$ or $PSL(2,\mathbb{Z})$.

Where can I find examples of these?

Another question: is there a good (ideally analytical, but possibly computer-aided) way to determine if a subgroup of the modular group generated by some given matrices has finite index, and possibly allowing to compute the index?

added "of finite index"
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Will Chen
Will Chen
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Are there noncongruence subgroups (of finite index) of the modular group generated only by 2 or 3 elements?

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Will Chen
Will Chen
  • 10.7k
  • 2
  • 32
  • 74

Are there noncongruence subgroups of the modular group generated only by 2 or 3 elements?

By the modular group I either mean $SL(2,\mathbb{Z})$, or $PSL(2,\mathbb{Z})$.

Where can I find examples of these?

Another question - is there a good (ideally analytical, but possibly computer-aided) way to determine if a subgroup of the modular group generated by some given matrices is finite index? (and then to compute the index?)

  • will