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A104453
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Smallest order for which there are n nonisomorphic finite Hamiltonian groups, or 0 if no such order exists.
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3
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8, 72, 216, 1800, 648, 5400, 1944, 88200, 27000, 16200, 10, 5832, 264600, 0, 48600, 17496, 10672200, 0, 1323000, 0, 793800, 20, 243000, 52488, 0, 32016600, 405000, 0, 9261000, 2381400, 0, 157464
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OFFSET
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1,1
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REFERENCES
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R. D. Carmichael, Introduction to the Theory of Groups of Finite Order, New York, Dover, 1956.
J. C. Lennox and S. E. Stonehewer, Subnormal Subgroups of Groups, Oxford University Press, 1987.
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LINKS
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Table of n, a(n) for n=1..32.
B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups, arXiv:math/0503183 [math.CO], 2005.
T. Pisanski and T.W. Tucker, The genus of low rank hamiltonian groups, Discrete Math. 78 (1989), 157-167.
Eric Weisstein's World of Mathematics, Abelian Group
Eric Weisstein's World of Mathematics, Hamiltonian Group
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FORMULA
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S_h(n) denotes the smallest number k for which exactly n nonisomorphic hamiltonian groups of order k exist. Here 0 indicates the case when n is not a product of partition numbers and S_h(n) does not exist.
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CROSSREFS
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Cf. A000688, A063966, A104488, A104407, A104404, A104452.
Sequence in context: A043932 A064015 A044576 * A254371 A143945 A239095
Adjacent sequences: A104450 A104451 A104452 * A104454 A104455 A104456
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KEYWORD
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nonn,hard
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AUTHOR
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Boris Horvat (Boris.Horvat(AT)fmf.uni-lj.si), Gasper Jaklic (Gasper.Jaklic(AT)fmf.uni-lj.si), Tomaz Pisanski, Apr 19 2005
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STATUS
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approved
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