Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T05:28:03.575Z Has data issue: false hasContentIssue false

Groups of small symmetric genus

Published online by Cambridge University Press:  18 May 2009

Coy L. May
Affiliation:
Department of Mathematics, Towson Stage UniversityBaltimore, Maryland 21204, U.S.A.
Jay Zimmerman
Affiliation:
Department of Mathematics, Towson Stage UniversityBaltimore, Maryland 21204, U.S.A.
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.

Group actions on compact surfaces have received considerable attention during the past century. The surface has often carried an analytic structure and been considered a Riemann surface or, equivalently, a complex algebraic curve.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Brin, M. G. and Squier, C. C., On the genus of Z3 × Z3 × Z3, European J. Combinatorics 5 (1988), 431443.CrossRefGoogle Scholar
2.Brin, M. G., Rauschenberg, D. E. and Squier, C. C., On the genus of the semidirect product of Z9, by Z3, J. Graph Theory 13 (1989), 4961.CrossRefGoogle Scholar
3.Bujalance, E. and Singerman, D., The symmetry type of a Riemann surface, Proc. London Math. Soc. (3) 51 (1985), 501519.CrossRefGoogle Scholar
4.Burnside, W., Theory of Groups of Finite Order, (Cambridge University Press, 1911).Google Scholar
5.Cannon, J. J., An introduction to the group theory language CAYLEY, Computational Group Theory (Atkinson, M., ed.), (Academic Press, 1984), 145183.Google Scholar
6.Conder, M. D. E., The symmetric genus of alternating and symmetric groups, J. Combin. Theory Ser. B 39 (1985), 179186.CrossRefGoogle Scholar
7.Conder, M. D. E., Hurwitz groups: a brief survey, Bull. Amer. Math. Soc. (N.S.) 23 (1990), 359370.CrossRefGoogle Scholar
8.Conder, M. D. E., Wilson, R. A. and Woldar, A. J., The symmetric genus of sporadic groups, Proc. Amer. Math. Soc. 116 (1992), 653663.CrossRefGoogle Scholar
9.Corn, D. and Singerman, D., Regular Hypermaps, European J. Combinatorics 9 (1988), 337351.CrossRefGoogle Scholar
10.Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete Groups, Fourth Edition, (Springer-Verlag, 1957).CrossRefGoogle Scholar
11.Garbe, D., Uber die regularen Zerlegungen geschlossener orientierbarer Flachen, J. Reine Angew. Math. 237 (1969), 3955.Google Scholar
12.Glover, H. and Sjerve, D., The genus of PSL2(q), J. Reine Angew. Math. 380 (1987), 5986.Google Scholar
13.Gross, J. L. and Tucker, T. W., Topological Graph Theory, (John Wiley and Sons, 1987).Google Scholar
14.Hurwitz, A., Uber algebraische gebilde mit eindeutigen transformationen in sich, Math. Ann. 41 (1893), 403442.CrossRefGoogle Scholar
15.May, C. L., Complex doubles of bordered Klein surfaces with maximal symmetry, Glasgow Math. J. 33 (1991), 6171.CrossRefGoogle Scholar
16.May, C. L., A lower bound for the real genus of a finite group, Canad J. Math, (to appear).Google Scholar
17.May, C. L. and Zimmerman, J., The symmetric genus of finite abelian groups, Illinois J. Math. 37 (1993) 400423.CrossRefGoogle Scholar
18.May, C. L. and Zimmerman, J., The symmetric genus of metacyclic groups, (to appear).Google Scholar
19.Maclachlan, C., Abelian groups of automorphisms of compact Riemann surfaces, Proc. London Math. Soc. 15 (1965), 699712.CrossRefGoogle Scholar
20.Pisanski, T. and White, A. T., Nonorientable embeddings of groups, European J. Combinatorics 9 (1988), 445461.CrossRefGoogle Scholar
21.Proulx, V. K., Classification of the toroidal groups, J. Graph Theory 2 (1978), 269273.CrossRefGoogle Scholar
22.Sherk, F. A., The regular maps on a surface of genus three, Canad. J. Math. 11 (1959), 452480.CrossRefGoogle Scholar
23.Singerman, D., On the structure of non-Euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974), 233240.CrossRefGoogle Scholar
24.Singerman, D., Symmetries of Riemann surfaces with large automorphism group, Math. Ann. 210 (1974), 1732.CrossRefGoogle Scholar
25.Tucker, T. W., Finite groups acting on surfaces and the genus of a group, J. Combin. Theory Ser. B 34 (1983), 8298.CrossRefGoogle Scholar
26.Tucker, T. W., There is one group of genus two, J. Combin. Theory Ser. B 36 (1984), 269275.CrossRefGoogle Scholar
27.White, A. T., Graphs, Groups and Surfaces, Revised Edition, (North-Holland, 1984).Google Scholar