Cortázar, IsmaelCosta González, Antonio Félix2025-12-232025-12-232019-01-01978-1-4704-4247-7https://hdl.handle.net/20.500.14468/31269A 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.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículo978-1-4704-5153-0