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A104453 Smallest order for which there are n nonisomorphic finite Hamiltonian groups, or 0 if no such order exists. 3
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; text; internal format)
OFFSET

1,1

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.

LINKS

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

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.

CROSSREFS

Cf. A000688, A063966, A104488, A104407, A104404, A104452.

Sequence in context: A043932 A064015 A044576 * A254371 A143945 A239095

Adjacent sequences:  A104450 A104451 A104452 * A104454 A104455 A104456

KEYWORD

nonn,hard

AUTHOR

Boris Horvat (Boris.Horvat(AT)fmf.uni-lj.si), Gasper Jaklic (Gasper.Jaklic(AT)fmf.uni-lj.si), Tomaz Pisanski, Apr 19 2005

STATUS

approved

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)