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Search: id:A104452
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| A104452 |
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Number of groups of order <= n all of whose subgroups are normal. |
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+0
4
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| 1, 2, 3, 5, 6, 7, 8, 12, 14, 15, 16, 18, 19, 20, 21, 27, 28, 30, 31, 33, 34, 35, 36, 40, 42, 43, 46, 48, 49, 50, 51, 59, 60, 61, 62, 66, 67, 68, 69, 73, 74, 75, 76, 78, 80, 81, 82, 88, 90, 92, 93, 95, 96, 99, 100, 104, 105, 106, 107, 109, 110, 111, 113, 125, 126, 127
(list; graph; listen)
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OFFSET
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1,2
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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, 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
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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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MATHEMATICA
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orders[n_]:=Map[Last, FactorInteger[n]]; a[n_]:=Apply[Times, Map[PartitionsP, orders[n]]]; e[n_]:=n/ 2^IntegerExponent[n, 2]; h[n_]/; Mod[n, 8]==0:=a[e[n]]; h[n_]:=0; numberOfAbelianGroupsOfOrderLEQThanN[n_]:=Map[Apply[Plus, # ]&, Table[Take[Map[a, Table[i, {i, 1, n}]], i], {i, 1, n}]]; numberOfHamiltonianGroupsOfOrderLEQThanN[n_]:=Map[Apply[Plus, # ]&, Table[Take[Map[h, Table[i, {i, 1, n}]], i], {i, 1, n}]]; numberOfAllGroupsOfOrderLEQThanN[n_]:=numberOfAbelianGroupsOfOrderLEQThanN[n] +numberOfHamiltonianGroupsOfOrderLEQThanN[n];
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CROSSREFS
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Cf. A000688, A063966, A104488, A104407, A104404, A104453.
Sequence in context: A006431 A151894 A028229 this_sequence A062877 A068526 A039086
Adjacent sequences: A104449 A104450 A104451 this_sequence A104453 A104454 A104455
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KEYWORD
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nonn,easy
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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 (Tomaz.Pisanski(AT)fmf.uni-lj.si), Apr 19 2005
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