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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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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.