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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| 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.
T. Pisanski, T.W. Tucker, The genus of low rank hamiltonian groups, Discrete Math. 78 (1989),157-167.
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LINKS
| B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups
Eric Weisstein's World of Mathematics, Abelian Group
Eric Weisstein's World of Mathematics, Hamiltonian Group
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FORMULA
| 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
| Cf. A000688, A063966, A104488, A104407, A104404, A104452.
Sequence in context: A043932 A064015 A044576 * A143945 A189954 A180288
Adjacent sequences: A104450 A104451 A104452 * A104454 A104455 A104456
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KEYWORD
| nonn,hard
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AUTHOR
| Boris Horvat (Boris.Horvat(AT)fmf.uni-lj.si), Gasper Jaklic (Gasper.Jaklic(AT)fmf.uni-lj.si), Tomaz Pisanski (Tomaz.Pisanski(AT)fmf.uni-lj.si), Apr 19 2005
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