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A347371
Number of isomorphism types of automorphism groups of Riemann surfaces of genus n.
5
19, 37, 44, 64, 59, 86, 65, 154, 119, 118, 98, 206, 99, 176, 139, 346, 117, 290, 136, 368, 187, 193, 171, 621, 184, 276, 306, 483, 187, 404, 189, 1014, 255, 332, 253, 880, 205, 381, 341, 1163, 244, 549, 244, 788, 436, 401, 273
OFFSET
2,1
COMMENTS
This includes subgroups of the full automorphism group.
Breuer's book erroneously gives a(33) = 1013. (See errata.)
REFERENCES
Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.
EXAMPLE
The 19 automorphism groups for Riemann surfaces of genus 2 are the trivial group, C2, C3, C4, C2 X C2, C5, C6, S3, Q8, C8, D8, C10, C6 . C2, C2 X C6, D12, QD16, SL_2(3), (C2 X C6) . C2, and GL_2(3). [Breuer, Table 9 on p. 77]
KEYWORD
nonn,hard
AUTHOR
Eric M. Schmidt, Aug 29 2021
STATUS
approved