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Finite 3-groups acting on bordered surfaces†

Published online by Cambridge University Press:  18 May 2009

Coy L. May
Coy L. May
Affiliation:
Department of Mathematics, Towson University Baltimore, Maryland 21252, USA E-mail: cmay@towson.edu
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Let G be a finite group. The real genus p(G) [8] is the minimum algebraic genus of any compact bordered Klein surface on which G acts. There are now several results about the real genus parameter. The groups with real genus p ≤ 5 have been classified [8,9,12], and genus formulas have been obtained for several classes of groups [8,9,10,11,12]. Most notably, McCullough calculated the real genus of each finite abelian group [13]. In addition, there is a good general lower bound for the real genus of a finite group [11].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 463 - 472
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Alling, N. L. and Greenleaf, N., Foundations of the theory of Klein surfaces, Lecture Notes in Mathematics No. 219 (Springer-Verlag, 1971).CrossRefGoogle Scholar
2.Bujalance, E., Etayo, J. J., Gamboa, J. M., and Gromadzki, G., Automorphism groups of compact bordered Klein surfaces, Lecture Notes in Mathematics No. 1439 (Springer-Verlag, 1990).CrossRefGoogle Scholar
3.Bujalance, E. and Gromadzki, G., On nilpotent groups of automorphisms of Klein surfaces, Proc. Amer. Math. Soc. 108 (1990), 749–759.CrossRefGoogle Scholar
4.Burnside, W., Theory of groups of finite order (Cambridge University Press, 1911).Google Scholar
5.Gorenstein, D., Finite groups (Harper and Row, 1968).Google Scholar
6.May, C. L., Automorphisms of compact Klein surfaces with boundary, Pacific J. Math. 59 (1975), 199–210.CrossRefGoogle Scholar
7.May, C. L., Large automorphisms groups of compact Klein surfaces with boundary, Glasgow Math.J. 18 (1977), 1–10.CrossRefGoogle Scholar
8.May, C. L., Finite groups acting on bordered surfaces and the real genus of a group, Rocky Mountain J. Math. 23 (1993), 707–724.CrossRefGoogle Scholar
9.May, C. L., The groups of real genus four, Michigan Math. J. 39 (1992), 219–228.CrossRefGoogle Scholar
10.May, C. L., Finite metacyclic groups acting on bordered surfaces, Glasgow Math. J. 36 (1994), 233–240.CrossRefGoogle Scholar
11.May, C. L., A lower bound for the real genus of a finite group, Canad. J. Math. 46 (1994), 1275–1286.CrossRefGoogle Scholar
12.May, C. L., The groups of small real genus, Houston Math. J. 20 (1994), 393–408.Google Scholar
13.McCullough, D., Minimal genus of abelian actions on Klein surfaces with boundary, Math Z. 205 (1990), 421–436.CrossRefGoogle Scholar
14.Singerman, D., On the structure of non-Euclidean crystallographic groups, Proc. Cambridge Philos, Soc. 76 (1974), 233–240.CrossRefGoogle Scholar