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Klein surfaces with maximal symmetry and their groups of automorphisms

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

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Abstract

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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