On automorphism groups of Riemann double covers of Klein surfaces

被引：3

作者：

Bujalance, E. ^{[1
]}

Cirre, F. J. ^{[1
]}

Conder, M. D. E. ^{[2
]}

机构：

[1] UNED, Fac Ciencias, Dept Matemat Fundamentales, C Senda del Rey S-N, Madrid 28040, Spain

[2] Univ Auckland, Dept Math, Private Bag 92019, Auckland 1142, New Zealand

来源：

JOURNAL OF ALGEBRA | 2017年 / 472卷

关键词：

Automorphisms Riemann surfaces; Fuchsian groups; Klein surfaces; Non-Euclidean crystallographic groups; CRYSTALLOGRAPHIC GROUPS; COMPLEX DOUBLES; NUMBER;

D O I：

10.1016/j.jalgebra.2016.09.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If G is a group of automorphisms of a compact Klein surface X, then. the direct product G X C-2 is a group of automorphisms of the Riemann double cover X+ of X. In this paper we analyse the relationship between G and the full groups of automorphisms Aut(X) and Aut(X+) of X and X+ respectively, in the special case where the group G is uniformised by a non-Euclidean crystallographic group with quadrangular signature (2, 2, 2, n). There is a difference in what happens between bordered surfaces and unbordered non-orientable surfaces, and so we consider those cases separately (including the special situation for n = 4 in the unbordered case). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：146 / 171

页数：26

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