Computational group theory has a history going back more than 80 years. It is a collaborative e ort of researchers in a wide range of areas in both mathematics and computer science. The eld has produced important algorithmic ideas and large software packages that have been used to obtain valuable results in mathematics and in other disciplines. The algorithmic achievements include the developme...

There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci 1995, Retor e 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities...

Last lecture, we learned about a combinatorial method for characterizing spaces: using simplicial complexes as triangulations of the spaces. We also showed how the connectivity of compact 2-manifolds is fully characterized by an invariant, the Euler characteristic, that may be computed using any triangulation of the space. In this lecture, we study group theory. This theory is part of the beaut...

C an one rotate only one corner piece in Rubik’s cube? What are the energy levels of the buckyball molecule? Are the graphs on Figure 1 isomorphic? What is the Galois group of the polynomial x8 + 2x7 + 28x6 + 1728x + 3456? What are the possible symmetry groups of crystals? These are all questions which, directly or in a not so obvious way, lead to problems in computational group theory. Algebra...

Thisnotedescrib esrecen tresearc h usingstructural propertiesofflnitegroupstodevise–cien talgorithms forgroupcomputation. 1991Mathematics SubjectClassiflcation: 20B40,20D05,68Q40 KeywordsandPhrases: grouptheoretic algorithms, implegroups

We introduce a novel approach for symmetry breaking by dominance detection (SBDD). The essence of SBDD is to perform ‘dominance checks’ at each node in a search tree to ensure that no symmetrically equivalent node has been visited before. While a highly effective technique for dealing with symmetry in constraint programs, SBDD forces a major overhead on the programmer, of writing a dominance ch...

Conformers of [M(ABC)6] complex have been enumerated on the basis of computational group theory, where M is the central metal, and ABC is the ligand, bound to M through A. Based on the 16 conformers of the M(AB)6 core unit, 7173 conformers have been found for the [M(ABC)6] complex, which are assigned to nine point groups, 1 D3d, 4 D3, 4 S6, 5 C2h, 7 C3, 182 C2, 15 Cs, 23 Ci, and 6932 C1.