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 A000019 Number of primitive permutation groups of degree n. (Formerly M0346 N0130) 16

%I M0346 N0130

%S 1,1,2,2,5,4,7,7,11,9,8,6,9,4,6,22,10,4,8,4,9,4,7,5,28,7,15,14,8,4,12,

%T 7,4,2,6,22,11,4,2,8,10,4,10,4,9,2,6,4,40,9,2,3,8,4,8,9,5,2,6,9,14,4,

%U 8,74,13,7,10,7,2,2,10,4,16,4,2,2,4,6,10,4,155,10,6,6,6,2,2,2,10,4,10,2

%N Number of primitive permutation groups of degree n.

%C A check found errors in Theissen's data (degree 121 and 125) as well as in Short's work (degree 169). - Alexander Hulpke (hulpke(AT)math.colostate.edu), Feb 19 2002

%C There is an error at n=574 in the Dixon-Mortimer paper. - Colva M. Roney-Dougal.

%D CRC Handbook of Combinatorial Designs, 1996, pp. 595ff.

%D J. D. Dixon and B. Mortimer, The primitive permutation groups of degree less than 1000, Math. Proc. Cambridge Philos. Soc., 103, 213-238, 1988 [But see comment above about errors! ]

%D K. Harada and H. Yamaki, The irreducible subgroups of GL_n(2) with n <= 6, C. R. Math. Rep. Acad. Sci. Canada 1, 1979, 75-78.

%D A. Hulpke, Konstruktion transitiver Permutationsgruppen, Dissertation, RWTH Aachen, 1996.

%D M. W. Short, The Primitive Soluble Permutation Groups of Degree less than 256, LNM 1519, 1992, Springer

%D C. C. Sims, Computational methods in the study of permutation groups, pp. 169-183 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D H. Thei{\ss}en, Eine Methode zur Normalisatorberechnung in Permutationsgruppen mit Anwendungen in der Konstruktion primitiver Gruppen, Dissertation, RWTH, RWTH-A, 1997 [But see comment above about errors! ]

%H N. J. A. Sloane, <a href="/A000019/b000019.txt">Table of n, a(n) for n=1..2499</a> [Computed using the GAP command shown below, which uses the results of Colva M. Roney-Dougal]

%H A. Hulpke, <a href="http://www.math.colostate.edu/~hulpke/smalldeg.html">Transitive groups of small degree</a>

%H A. Hulpke, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.5038">Constructing transitive permutation groups</a>, J. Symbolic Comput. 39 (2005), 1-30.

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%H <a href="/index/Cor#core">Index entries for "core" sequences</a>

%o (GAP) List([2..2499],NrPrimitiveGroups);

%o (MAGMA) [NumberOfPrimitiveGroups(i) : i in [1..999]];

%Y Cf. A000001, A023675, A023676, A000638, A002106, A005432, A000637.

%K nonn,core,nice

%O 1,3

%A _N. J. A. Sloane_.

%E More terms and additional references from Alexander Hulpke (Alexander.Hulpke(AT)Math.RWTH-Aachen.DE)

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