MAPS OF SURFACE GROUPS TO FINITE GROUPS WITH NO SIMPLE LOOPS IN THE KERNEL
2000 ◽
Vol 09
(08)
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pp. 1029-1036
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Keyword(s):
Let Fg denote the closed orientable surface of genus g. What is the least order finite group, Gg, for which there is a homomorphism ψ:π1(Fg)→Gg so that nontrivial simple closed curve on Fg represents an element in Ker (ψ)? For the torus it is easily seen that G1=Z2×Z2 suffices. We prove here that G2 is a group of order 32 and that an upper bound for the order of Gg is given by g2g+1. The previously known upper bound was greater than 2g22g.
Keyword(s):
2006 ◽
Vol 74
(1)
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pp. 121-132
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Keyword(s):
1969 ◽
Vol 9
(3-4)
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pp. 467-477
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Keyword(s):
2017 ◽
Vol 16
(03)
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pp. 1750043
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1973 ◽
Vol 9
(2)
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pp. 267-274
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2016 ◽
Vol 15
(10)
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pp. 1650197
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Keyword(s):
2018 ◽
Vol 97
(2)
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pp. 229-239
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