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Klein surfaces with maximal symmetry and their groups of automorphisms



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Etayo Gordejuela, J. Javier (1984) Klein surfaces with maximal symmetry and their groups of automorphisms. Mathematische Annalen, 268 (4). pp. 533-538. ISSN 0025-5831

Official URL: http://www.springerlink.com/content/k332112h2292272q/



A Klein surface X is a surface with a dianalytic structure. If its topological genus is g and it has k boundary components then its algebraic genus is p=2g+k−1 (X orientable) and p=g+k−1 (X nonorientable). A Klein surface of algebraic genus p has at most 12(p−1) automorphisms and if this bound is attained then AutX is called an M ∗ -group. In this paper the author finds families of M ∗ -groups and determines the topological type of the surface on which they act. The groups he deals with are those of the form G m,n,q considered by H. M. S. Coxeter [Trans. Amer. Math. Soc. 45 (1939), 73--150; Zbl 20, 207]: PSL(2,q), q≡1mod4, PGL(2,q), q≡3mod4 and PSL(2,2 m ) . For related work see a paper by N. Greenleaf and C. L. May [ibid. 274 (1982), no. 1, 265--283]

Item Type:Article
Uncontrolled Keywords:Classification theory of Riemann surfaces; Coverings, fundamental group; Other matrix groups over fields
Subjects:Sciences > Mathematics > Functions
ID Code:15738
Deposited On:22 Jun 2012 11:09
Last Modified:22 Jun 2012 11:09

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