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Complex doubles of bordered Klein surfaces with maximal symmetry

Published online by Cambridge University Press:  18 May 2009

Coy L. May
Coy L. May
Affiliation:
Department of Mathematics, Towson State University, Towson, Maryland 21204-7097, USA
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A compact bordered Klein surface X of algebraic genus g ≥ 2 has maximal symmetry [6] if its automorphism group A(X) is of order 12(g — 1), the largest possible. The bordered surfaces with maximal symmetry are clearly of special interest and have been studied in several recent papers ([6] and [9] among others).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 61 - 71
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Alling, N. L. and Greenleaf, N., Foundations of the theory of Klein surfaces, Lecture Notes in Mathematics Vol. 219 (Springer-Verlag, 1971).CrossRefGoogle Scholar
2.Bujalance, E., Normal N.E.C. signatures, Illinois J. Math. 26 (1982), 519–530.CrossRefGoogle Scholar
3.Bujalance, E. and Singerman, D., The symmetry type of a Riemann surface, Proc. London Math. Soc. (3) 51 (1985), 501–519.CrossRefGoogle Scholar
4.Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete Band 14 (Springer-Verlag, 1972).Google Scholar
5.Garbe, D., Uber die regularen Zerlegungen geschlossener orientierbarer Flachen, J. Reine Angew. Math. 237 (1969), 39–55.Google Scholar
6.Greenleaf, N. and May, C. L., Bordered Klein surfaces with maximal symmetry, Trans. Atner. Math. Soc. 274 (1982), 265–283.CrossRefGoogle Scholar
7.Macbeath, A. M., The classification of non-Euclidean plane crystallographic groups, Canad. J. Math. 19 (1966), 1192–1205.CrossRefGoogle Scholar
8.May, C. L., Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977), 1–10.CrossRefGoogle Scholar
9.May, C. L., The species of bordered Klein surfaces with maximal symmetry of low genus, Pacific J. Math. 111 (1984), 371–394.CrossRefGoogle Scholar
10.Rose, J. S., A course on group theory (Cambridge University Press, 1978).Google Scholar
11.Sah, C. H., Groups related to compact Riemann surfaces, Ada Math. 123 (1969), 13–42.Google Scholar
12.Sherk, F. A., The regular maps on a surface of genus three, Canad. J. Math. 11 (1959), 452–480.CrossRefGoogle Scholar
13.Singerman, D., On the structure of non-Euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974), 233–240.CrossRefGoogle Scholar
14.Singerman, D., Finitely maximal Fuchsian groups, J. London Math. Soc. (2) 6 (1972), 29–38.CrossRefGoogle Scholar
15.Singerman, D., Symmetries of Riemann surfaces with large automorphism group, Math. Ann. 210 (1974), 17–32.CrossRefGoogle Scholar
16.Singerman, D., private communication, 1988.Google Scholar