Abelian actions on compact nonorientable Riemann surfaces
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Abstract Given an integer $g>2$ , we state necessary and sufficient conditions for a finite Abelian group to act as a group of automorphisms of some compact nonorientable Riemann surface of genus g. This result provides a new method to obtain the symmetric cross-cap number of Abelian groups. We also compute the least symmetric cross-cap number of Abelian groups of a given order and solve the maximum order problem for Abelian groups acting on nonorientable Riemann surfaces.
1994 ◽
Vol 36
(1)
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pp. 17-32
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2015 ◽
Vol 25
(05)
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pp. 889-897
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1981 ◽
Vol 90
(2)
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pp. 273-278
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1975 ◽
Vol 18
(1)
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pp. 57-60
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1971 ◽
Vol 12
(2)
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pp. 187-192
2011 ◽
Vol 12
(01n02)
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pp. 125-135
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2019 ◽
Vol 150
(4)
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pp. 1937-1964
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