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Algorithms for Groups
, 1994
"... Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational group theory may be used to gain insight into the general str ..."
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Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational group theory may be used to gain insight into the general structure of algebraic algorithms. This paper examines the basic ideas behind some of the more important algorithms for finitely presented groups and permutation groups, and surveys recent developments in these fields.
ALGORITHMIC RECOGNITION OF ACTIONS OF 2HOMOGENEOUS GROUPS ON PAIRS
, 1998
"... We give an algorithm that takes as input a transitive permutation group (G, Ω) of degree n = �m � 2, and decides whether or not Ω is Gisomorphic to the action of G on the set of unordered pairs of some set Ɣ on which G acts 2homogeneously. The algorithm is constructive: if a suitable action exists, ..."
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We give an algorithm that takes as input a transitive permutation group (G, Ω) of degree n = �m � 2, and decides whether or not Ω is Gisomorphic to the action of G on the set of unordered pairs of some set Ɣ on which G acts 2homogeneously. The algorithm is constructive: if a suitable action exists, then one such will be found, together with a suitable isomorphism. We give a deterministic O(snlogc n) implemention of the algorithm that assumes advance knowledge of the suborbits of (G, Ω). This leads to deterministic O(sn²) and MonteCarlo O(snlogc n) implementations that do not make this assumption.