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August 6th, 2012, 12:23 PM   #1
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Identifying a Subgroup via a Permutation Representation

Dear Forum,

Suppose we have a known group G and an unknown subgroup H. The permutation representation of G on the cosets of H gives a permutation group C, which is known. Is it possible to identify the generators of H using this information? If so, how? If not, what further information is needed?

(For background, my G is the modular group PSL(2,Z); H is a not-necessarily-congruence subgroup of G. In the literature C is sometimes called a "cartographic group").

Many thanks,

James
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