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2019-01-01
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info:eu-repo/semantics/openAccess
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Editorial
American Mathematical Society
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Resumen
A planar Euclidean or hyperbolic crystallographic group is a
subgroup of the group of isometries of the Euclidean plane JE2 , respectively the
hyperbolic plane IHI2, with compact orbit space. These groups are classified
algebraically by a symbol called signature and an equivalence relation defined
on the set of signatures. In 1990 A.H.M. Hoare gave an algorithm to obtain
the signature of a finite index subgroup of a planar crystallographic group.
Recently the authors completed the algorithm of Hoare and implemented it
on a computer system.
In the signature of the hyperbolic groups there is a sign + or - , in the
case of + sign the cyclic arder on sorne integers in signatures are essential to
determine the isomorphism class. In this article we show examples where such
cyclic arder is necessary to determine if two subgroups of a given hyperbolic
group are isomorphic. Finally we announce the implementation of the algorithm
to compute the signature of subgroups of hyperbolic crystallographic
groups on the computer system far group theory GAP.
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Categorías UNESCO
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Centro
Facultad de Ciencias
Departamento
Matemáticas Fundamentales