THE SYMMETRIC GENUS OF 2-GROUPS
2012 ◽
Vol 55
(1)
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pp. 9-21
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AbstractLet G be a finite group. The symmetric genus σ(G) is the minimum genus of any Riemann surface on which G acts faithfully. We show that if G is a group of order 2m that has symmetric genus congruent to 3 (mod 4), then either G has exponent 2m−3 and a dihedral subgroup of index 4 or else the exponent of G is 2m−2. We then prove that there are at most 52 isomorphism types of these 2-groups; this bound is independent of the size of the 2-group G. A consequence of this bound is that almost all positive integers that are the symmetric genus of a 2-group are congruent to 1 (mod 4).
2010 ◽
Vol 09
(03)
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pp. 465-481
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2015 ◽
Vol 67
(4)
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pp. 848-869
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1981 ◽
Vol 30
(3)
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pp. 257-263
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1983 ◽
Vol 28
(1)
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pp. 101-110
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2002 ◽
Vol 01
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pp. 267-279
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2019 ◽
Vol 18
(01)
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pp. 1950013
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1999 ◽
Vol 41
(1)
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pp. 115-124
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1995 ◽
Vol 117
(1)
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pp. 137-151
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