Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-28T18:59:32.902Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological types of Klein surfaces with a maximum order automorphism

Published online by Cambridge University Press:  18 May 2009

J. A. Bujalance
J. A. Bujalance
Affiliation:
Dep. de Matematicas, Centro Universitario de Toledo, Toledo, Spain
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If X is a Klein surface (KS) with boundary, of algebraic genus p, and Φ is an automorphism of order N, May [8] proved that N ≤ 2p + 2 when X is orientable and p is even, and N ≤ 2p otherwise.

He proved also that the unique topological type of an orientable KS having an orientation-preserving automorphism of maximum order is a surface with one boundary component when p is even, with two boundary components when p is odd.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 87 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Ailing, N. L. and Greenleaf, N., Foundations of the theory of Klein surfaces, Lecture Notes in Mathematics 219 (Springer, 1971).CrossRefGoogle Scholar
2.Bujalance, E., Proper periods of normal NEC subgroups with even index, Rev. Mat. Hisp.-Amer. (4) 41 (1981), 121–127.Google Scholar
3.Bujalance, J. A., Normal subgroups of even index of an NEC group, Arch. Math. (Basel), to appear.Google Scholar
4.Etayo, J. J., On the order of automorphism groups of Klein surfaces, Glasgow Math. J. 26 (1985), 75–81.Google Scholar
5.Hoare, A. H. M. and Singerman, D., The orientability of subgroups of plane groups, in Campbell, C. M. and Robertson, E. F., eds., Groups-St. Andrews 1981, London Mathematical Society Lecture Note Series 71 (Cambridge, 1982), 221–227.CrossRefGoogle Scholar
6.Macbeath, A. M., The classification of non-euclidean plane crystallographic groups, Canad. J. Math. 6 (1967), 1192–1205.CrossRefGoogle Scholar
7.May, C. L., Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977), 1–10.CrossRefGoogle Scholar
8.May, C. L., Cyclic automorphism groups of compact bordered Klein surfaces, Houston J. Math. 3 (1977), 395–405.Google Scholar
9.Preston, R., Projective structures and fundamental domains on compact Klein surfaces (University of Texas Ph.D. thesis, 1975).Google Scholar
10.Singerman, D., On the structure of non-euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974), 233–240.CrossRefGoogle Scholar
11.Wilkie, M. C., On non-euclidean crystallographic groups, Math. Z. 91 (1966), 87–102.CrossRefGoogle Scholar