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In 1995 it was proved by Gonz$\acute{a}$lez-Diez that the cyclic group generated by a p-gonal automorphism of a closed Riemann surface of genus at least two is unique up to conjugation in the full group of conformal automorphisms. Later, in 2008, Gromadzki provided a different and shorter proof of the same fact using the Castelnuovo-Severi theorem. In this paper we provide another proof which is shorter and is just a simple use of Sylow's theorem together with the Castelnuovo-Severi theorem. This method permits to obtain that the cyclic group generated by a conformal automorphism of order p of a handlebody with a Kleinian structure and quotient the three-ball is unique up to conjugation in the full group of conformal automorphisms.
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참고문헌 (8)
참고문헌 신청
A. Wootton / 2007 / The full automorphism group of a cyclic p-gonal surface / J. Algebra 312 (1) : 377 ~ 396
B. Maskit / 1987 / Kleinian Groups, GMW / Springer-Verlag
D. Singerman / 1972 / Finitely maximal Fuchsian groups / J. London Math. Soc. (2) 6 : 29 ~ 38
G. Castelnuovo / / Sulle serie algebriche si gruppi di punti appartenenti ad una curve al- gebraica / Rend. Real Accad. Lincei (5) 15 : 509 ~
G. Gonzalez-Diez / 1995 / On prime Galois coverings of the Riemann sphere / Ann. Math. Pura Appl. (4) 168 : 1 ~ 15
B. Maskit / 1987 / Kleinian Groups, GMW / Springer-Verlag
D. Singerman / 1972 / Finitely maximal Fuchsian groups / J. London Math. Soc. (2) 6 : 29 ~ 38
G. Castelnuovo / / Sulle serie algebriche si gruppi di punti appartenenti ad una curve al- gebraica / Rend. Real Accad. Lincei (5) 15 : 509 ~
G. Gonzalez-Diez / 1995 / On prime Galois coverings of the Riemann sphere / Ann. Math. Pura Appl. (4) 168 : 1 ~ 15
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