THE STRONG SYMMETRIC GENUS OF DIRECT PRODUCTS
2011 ◽
Vol 10
(05)
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pp. 901-914
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Let G be a finite group. The strong symmetric genus σ0(G) is the minimum genus of any Riemann surface on which G acts faithfully and preserving orientation. Assume that G is non-abelian and generated by two elements, one of which is an involution, and that n is relatively prime to |G|. Our first main result is the determination of the strong symmetric genus of the direct product Zn ×G in terms of n, |G|, and a parameter associated with the group G. We obtain a variety of genus formulas. Finally, we apply these results to prove that for each integer g ≥ 2, there are at least four groups of strong symmetric genus g.
1955 ◽
Vol 51
(1)
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pp. 25-36
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1988 ◽
Vol 31
(3)
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pp. 469-474
2015 ◽
Vol 67
(4)
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pp. 848-869
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1956 ◽
Vol 52
(1)
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pp. 5-11
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1968 ◽
Vol 20
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pp. 1300-1307
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1974 ◽
Vol 17
(1)
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pp. 129-130
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1999 ◽
Vol 60
(2)
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pp. 177-189
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2012 ◽
Vol 55
(1)
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pp. 9-21
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