Computational group theory | Finite groups

Black box group

In computational group theory, a black box group (black-box group) is a group G whose elements are encoded by bit strings of length N, and group operations are performed by an oracle (the "black box"). These operations include: • taking a product g·h of elements g and h,• taking an inverse g−1 of element g,• deciding whether g = 1. This class is defined to include both the permutation groups and the matrix groups. The upper bound on the order of G given by |G| ≤ 2N shows that G is finite. (Wikipedia).

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Related pages

Bit array | Order (group theory) | Permutation group | Group representation | Quantum algorithm | Oracle machine | Schreier–Sims algorithm | Property testing | Implicit graph | Matroid oracle | Computational group theory | Finite group | Group (mathematics)