Proper periods of normal N.E.C. subgroups with even index.

Emilio Bujalance

Revista Matemática Hispanoamericana (1981)

  • Volume: 41, Issue: 5-6, page 121-127
  • ISSN: 0373-0999

Abstract

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By a non-Euclidean crystallographic (N.E.C.) group we shall mean a discrete subgroup Γ of isometries of the non-Euclidean plane including those reverse orientation, reflections and glide-reflections.In [1] we computed the proper periods of normal N.E.C. subgroups of an N.E.C. group, when the index of the group with respect to the subgroup is odd. In this paper we shall compute the proper period of normal N.E.C. subgroups, when the index is even.The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Maclachan [4].

How to cite

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Bujalance, Emilio. "Proper periods of normal N.E.C. subgroups with even index.." Revista Matemática Hispanoamericana 41.5-6 (1981): 121-127. <http://eudml.org/doc/39785>.

@article{Bujalance1981,
abstract = {By a non-Euclidean crystallographic (N.E.C.) group we shall mean a discrete subgroup Γ of isometries of the non-Euclidean plane including those reverse orientation, reflections and glide-reflections.In [1] we computed the proper periods of normal N.E.C. subgroups of an N.E.C. group, when the index of the group with respect to the subgroup is odd. In this paper we shall compute the proper period of normal N.E.C. subgroups, when the index is even.The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Maclachan [4].},
author = {Bujalance, Emilio},
journal = {Revista Matemática Hispanoamericana},
keywords = {Grupo cristalográfico no euclídeo; Período propio; discrete non-Euclidean crystallographic group; branched cover; quotient surface; branching order; elliptic elements; periods},
language = {eng},
number = {5-6},
pages = {121-127},
title = {Proper periods of normal N.E.C. subgroups with even index.},
url = {http://eudml.org/doc/39785},
volume = {41},
year = {1981},
}

TY - JOUR
AU - Bujalance, Emilio
TI - Proper periods of normal N.E.C. subgroups with even index.
JO - Revista Matemática Hispanoamericana
PY - 1981
VL - 41
IS - 5-6
SP - 121
EP - 127
AB - By a non-Euclidean crystallographic (N.E.C.) group we shall mean a discrete subgroup Γ of isometries of the non-Euclidean plane including those reverse orientation, reflections and glide-reflections.In [1] we computed the proper periods of normal N.E.C. subgroups of an N.E.C. group, when the index of the group with respect to the subgroup is odd. In this paper we shall compute the proper period of normal N.E.C. subgroups, when the index is even.The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Maclachan [4].
LA - eng
KW - Grupo cristalográfico no euclídeo; Período propio; discrete non-Euclidean crystallographic group; branched cover; quotient surface; branching order; elliptic elements; periods
UR - http://eudml.org/doc/39785
ER -

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