A bound for the number of automorphisms of a compact Klein surface with boundary

May, Coy L.

doi:10.1090/S0002-9939-1977-0435385-0

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ISSN 1088-6826(online) ISSN 0002-9939(print)

A bound for the number of automorphisms of a compact Klein surface with boundary

Author: Coy L. May
Journal: Proc. Amer. Math. Soc. 63 (1977), 273-280
MSC: Primary 30A46; Secondary 14H30, 32L05
MathSciNet review: 0435385
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Abstract: For an integer $g \geqslant 2$ , let $\nu (g)$ be the order of the largest group of automorphisms of a compact Klein surface with nonempty boundary of genus g. We show that $\nu (g) \geqslant 4(g + 1)$ for all g and that for an infinite number of values of $\nu (g) = 4(g + 1)$ .

[1] Robert D. M. Accola, On the number of automorphisms of a closed Riemann surface, Trans. Amer. Math. Soc. 131 (1968), 398–408. MR 0222281 (36 #5333), http://dx.doi.org/10.1090/S0002-9947-1968-0222281-6
[2] Norman L. Alling and Newcomb Greenleaf, Foundations of the theory of Klein surfaces, Lecture Notes in Mathematics, Vol. 219, Springer-Verlag, Berlin, 1971. MR 0333163 (48 #11488)
[3] Maurice Heins, On the number of 1-1 directly conformal maps which a multiply-connected plane region of finite connectivity 𝑝(>2) admits onto itself, Bull. Amer. Math. Soc. 52 (1946), 454–457. MR 0016469 (8,21d), http://dx.doi.org/10.1090/S0002-9904-1946-08590-0
[4] A. Hurwitz, Ueber algebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann. 41 (1892), no. 3, 403–442 (German). MR 1510753, http://dx.doi.org/10.1007/BF01443420
[5] Takao Kato, On the number of automorphisms of a compact bordered Riemann surface, Kōdai Math. Sem. Rep. 24 (1972), 224–233. MR 0306484 (46 #5610)
[6] C. Maclachlan, A bound for the number of automorphisms of a compact Riemann surface., J. London Math. Soc. 44 (1969), 265–272. MR 0236378 (38 #4674)
[7] Coy L. May, Automorphisms of compact Klein surfaces with boundary, Pacific J. Math. 59 (1975), no. 1, 199–210. MR 0399451 (53 #3295)
[8] Coy L. May, Large automorphism groups of compact Klein surfaces with boundary. I, Glasgow Math. J. 18 (1977), no. 1, 1–10. MR 0425113 (54 #13071)
[9] -, Cyclic automorphism groups of compact Klein surfaces with boundary (to appear).
[10] Kôtaro Oikawa, Notes on conformal mappings of a Riemann surface onto itself, Kōdai Math. Sem. Rep. 8 (1956), 23–30. MR 0080730 (18,290d)
[11] W. R. Scott, Group theory, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964. MR 0167513 (29 #4785)
[12] Ryōhei Tsuji, On conformal mapping of a hyperelliptic Riemann surface onto itself., Kōdai Math. Sem. Rep. 10 (1958), 127–136. MR 0100085 (20 #6521)

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