Hidden Subgroup Zoo

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Let <math>f</math>  be function from a group <math>G</math> to a set <math>S</math> which is promised  to be constant and  distinct on different left cosets of an unknown subgroup <math>H</math> : <math>f(g)=f(h)</math> iff <math>gH = gH</math> . The goal of the hidden subgroup problem is, by querying <math>f</math>, to identify the 

subgroup <math>H</math>.