ABELIAN p-GROUPS OF SYMMETRIES OF SURFACES

Date

2011-06-01

Author

Talu, Emine Yasemin

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An integer g >= 2 is said to be a genus of a finite group G if there is a compact Riemann surface of genus g on which G acts as a group of automorphisms. In this paper finite abelian p-groups of arbitrarily large rank, where p is an odd prime, are investigated. For certain classes of abelian p-groups the minimum reduced stable genus sigma(0) of G is calculated and consequently the genus spectrum of G is completely determined for certain "extremal" abelian p-groups. Moreover for the case of Z(p)(r1) circle plus Z(p2)(r2) we will see that the genus spectrum determines the isomorphism class of the group uniquely.

Subject Keywords

Genus spectrum, Minimum reduced stable genus, Symmetries of surfaces

URI

https://hdl.handle.net/11511/36648

Journal

TAIWANESE JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.11650/twjm/1500406290

Collections

Department of Mathematics, Article

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Citation Formats

E. Y. Talu, “ABELIAN p-GROUPS OF SYMMETRIES OF SURFACES,” TAIWANESE JOURNAL OF MATHEMATICS, pp. 1129–1140, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36648.