Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 324 / 1 / a / Solution

The hidden subgroup problem for a group $G$ is specified by an oracle $f:G\to S$ that hides an unknown subgroup $H\le G$: it is constant on each left coset of $H$ and takes distinct values on distinct cosets. The task is to determine $H$, usually by finding a generating set for it.