Backtrack Search Algorithm Using First in Orbit A group G with the base B=[I, 2...k] and a powerful generating set S are the inputs. Additionally, there is a decidable property P, whose members make up a subgroup. The procedure search(G: group; P: property; s: 1..k+l; var K: group); (* Search G (s) for the subgroup K of elements fulfilling P. *) produces a strong generating set relative to B for the subgroup K =H(P).

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