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), 273280
MSC:
Primary 30A46; Secondary 14H30, 32L05
MathSciNet review:
0435385
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Abstract: For an integer , let be the order of the largest group of automorphisms of a compact Klein surface with nonempty boundary of genus g. We show that for all g and that for an infinite number of values of .
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 M. Heins, On the number of directly conformal maps which a multiplyconnected plane region of finite connectivity admits onto itself, Bull. Amer. Math. Soc. 52 (1946), 454457. MR 8, 21. MR 0016469 (8:21d)
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 A. Hurwitz, Über algebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann. 41 (1893), 403442. MR 1510753
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 C. Maclachlan, A bound for the number of automorphisms of a compact Riemann surface, J. London Math. Soc. 44 (1969), 265272. MR 38 #4674. MR 0236378 (38:4674)
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 C. L. May, Automorphisms of compact Klein surfaces with boundary, Pacific J. Math. 59 (1975), 199210. MR 0399451 (53:3295)
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 , Large automorphism groups of compact Klein surfaces with boundary. I, Glasgow Math. J. 18 (1977), 110. MR 0425113 (54:13071)
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 , Cyclic automorphism groups of compact Klein surfaces with boundary (to appear).
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 W. R. Scott, Group theory, PrenticeHall, Englewood Cliffs, N.J., 1964. MR 29 #4785. MR 0167513 (29:4785)
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 R. Tsuji, On conformal mapping of a hyperelliptic Riemann surface onto itself, Kōdai Sem. Rep. 10 (1958), 127136. MR 20 #6521. MR 0100085 (20:6521)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197704353850
PII:
S 00029939(1977)04353850
Keywords:
Klein surface,
automorphism group,
algebraic genus,
complex double,
Riemann surface,
ramified covering,
Hurwitz ramification formula
Article copyright:
© Copyright 1977
American Mathematical Society
