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Discrete groups of Wq-symmetry
by
Alexandru Lungu
State University of Moldova, Chisinau, Republic of Moldova
In the case of Wp-symmetry the transformations of the qualities, attributed to the points, essentially depend on the choice of points. The transformation of [`P]-symmetry g(p) is composed from the components g and p, where g is transformation of symmetry which operates both on points and on qualities, attributed to the points, by the given rule independent of the points and p is a supplementary transformation of these qualities. Wq-symmetry is a generalization of [`P]-symmetry, obtained as a rezult of setting the problems of Wp-symmetry and [`P]-symmetry.
The groups of Wq-symmetry are subgroups of the crossed standard Cartesian wreath product of initial group P of permutations and discrete group G of classical symmetry (as their generating), accompanied with homomorphism \tau: G --> AutW.
The methods of deriving the groups of A.M.Zamorzaev's P-symmetry of different types are bazed on homomorphic mapping and its properties. The solution of analogous problems for Wq-symmetry demands the generalization of homomorphisms as the crossed quasihomomorphism. Moreover, it requires the investigation of some their properties.
Date received: February 28, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caet-06.