Taiwanese Journal of Mathematics

Abelian $p$-Groups of Symmetries of Surfaces

Y. Talu

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An integer $g \geq 2$ 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 $Z_p^{r_1} \oplus Z_{p^2}^{r_2}$ we will see that the genus spectrum determines the isomorphism class of the group uniquely.

Article information

Taiwanese J. Math., Volume 15, Number 3 (2011), 1129-1140.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 57M60: Group actions in low dimensions
Secondary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx] 30F35: Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]

genus spectrum minimum reduced stable genus symmetries of surfaces


Talu, Y. Abelian $p$-Groups of Symmetries of Surfaces. Taiwanese J. Math. 15 (2011), no. 3, 1129--1140. doi:10.11650/twjm/1500406290. https://projecteuclid.org/euclid.twjm/1500406290

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