Cyclic p-groups of symmetries of surfaces
Glasgow mathematical journal, Tome 33 (1991) no. 2, pp. 213-221

Voir la notice de l'article provenant de la source Cambridge University Press

Let Σg denote a compact orientable surface of genus g ≥ 2. We consider finite groups G acting effectively on Σg and preserving the orientation—for short, G acts on Σg or Gis a symmetry group of Σg. Each surface Σg admits only finitely many symmetry groups G and the orders of these groups are bounded by Wiman's bound of 84(g – 1). This bound is attained for infinitely many values of g [12], see also [9], and all values of g ≤ 104 for which it is attained are known [4].
Kulkarni, Ravi S.; Maclachlan, Colin. Cyclic p-groups of symmetries of surfaces. Glasgow mathematical journal, Tome 33 (1991) no. 2, pp. 213-221. doi: 10.1017/S0017089500008247
@article{10_1017_S0017089500008247,
     author = {Kulkarni, Ravi S. and Maclachlan, Colin},
     title = {Cyclic p-groups of symmetries of surfaces},
     journal = {Glasgow mathematical journal},
     pages = {213--221},
     year = {1991},
     volume = {33},
     number = {2},
     doi = {10.1017/S0017089500008247},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008247/}
}
TY  - JOUR
AU  - Kulkarni, Ravi S.
AU  - Maclachlan, Colin
TI  - Cyclic p-groups of symmetries of surfaces
JO  - Glasgow mathematical journal
PY  - 1991
SP  - 213
EP  - 221
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008247/
DO  - 10.1017/S0017089500008247
ID  - 10_1017_S0017089500008247
ER  - 
%0 Journal Article
%A Kulkarni, Ravi S.
%A Maclachlan, Colin
%T Cyclic p-groups of symmetries of surfaces
%J Glasgow mathematical journal
%D 1991
%P 213-221
%V 33
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008247/
%R 10.1017/S0017089500008247
%F 10_1017_S0017089500008247

[1] 1.Accola, R. D. M., On the number of automorphisms of a closed Riemann surface. Trans. Amer. Math. Soc. 131 (1968), 398–408. Google Scholar | DOI

[2] 2.Chetiya, B. P., On genuses of compact Riemann surfaces admitting solvable automorphism groups. Indian J. Pure appl. Math. 12 (1981), 1312–1318. Google Scholar

[3] 3.Conder, M. D. E., Generators for alternating and symmetric groups. J. London Math. Soc. 22 (1980), 75–86. Google Scholar | DOI

[4] 4.Conder, M. D. E., The genus of Compact Riemann surfaces with Maximal Automorphism Group. J. of Algebra 108 (1987), 204–247. Google Scholar | DOI

[5] 5.Glover, H. and Mislin, G., Torsion in the mapping class group and its cohomology. J. of Pure & Appl. Algebra 44 (1987), 177–189. Google Scholar | DOI

[6] 6.Glover, H. and Sjerve, D., The genus of PSL(q) J. Reine und Angew Math. 380 (1987), 59–86. Google Scholar

[7] 7.Harvey, W. J., Cyclic groups of automorphisms of a compact Riemann surface. Quart. J. Math. 17 (1966), 86–97. Google Scholar | DOI

[8] 8.Kulkarni, R. S., Symmetries of surfaces. Topology 26 (1987), 195–203. Google Scholar | DOI

[9] 9.Kulkarni, R. S., Normal subgroups of fuchsian groups. Quart. J. Math. Oxford 36 (1985), 325–344. Google Scholar | DOI

[10] 10.Kuribayashi, A. and Kimura, H., On Automorphism Groups of Compact Riemann surfaces of Genus 5. Proc. Japan Academy 63 Ser A (1987), 126–130. Google Scholar

[11] 11.Kuribayashi, I. and Kuribayashi, A., On Automorphism groups of a Compact Riemann Surface of genus 4 as subgroups in GL(4, C). Bull. Facul. Sc. Eng. Chuo Univ. 28 (1985), 11–28. Google Scholar

[12] 12.Macbeath, A. M., On a Theorem of Hurwitz Proc. Glasgow Math. Assoc. 5 (1961), 90–96. Google Scholar | DOI

[13] 13.Maclachlan, C., Groups of Automorphisms of compact Riemann surfaces Ph.D. Thesis Birmingham Univ. 1966. Google Scholar

[14] 14.Maclachlan, C., Abelian groups of automorphisms of compact Riemann surfaces. Proc. London Math. Soc. 15 (1965), 699–712. Google Scholar | DOI

[15] 15.Maclachlan, C., A bound for the number of automorphisms of a compact Riemann surface. J. London Math. Soc. 44 (1969), 265–272. Google Scholar | DOI

[16] 16.McCullough, D., Miller, A. and Zimmermann, B., Group actions on non-closed 2-manifolds (to appear). Google Scholar

[17] 17.Wiman, A., Uber die hyperelliptischen Kurven und diejenigen vom Geschlechte p = 3, welche eindeutigen Transformationen in sich Zulassen Bihang. Till Kongl. Svenska Veienskaps—Akademiems Hadlingar (Stockholm 1895–6), 21, 1–23. Google Scholar

[18] 18.Zomorrodian, R., Nilpotent automorphism groups of Riemann surfaces, Trans. Amer. Math. Soc. 288 (1985), 241–255. Google Scholar

Cité par Sources :