Search: id:A000019
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%I A000019 M0346 N0130
%S A000019 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 A000019 7,4,2,6,22,11,4,2,8,10,4,10,4,9,2,6,4,40,9,2,3,8,4,8,9,5,2,6,9,14,4,8,
%U A000019 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 A000019 Number of primitive permutation groups of degree n.
%C A000019 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 A000019 There is an error at n=574 in the Dixon-Mortimer paper. - Colva M. Roney-Dougal.
%D A000019 CRC Handbook of Combinatorial Designs, 1996, pp. 595ff.
%D A000019 J. D. Dixon and B. Mortimer, The primitive permutation groups of deg 
               ree less than 1000, Math. Proc. Cambridge Philos. Soc., 103, 213-238, 
               1988 [But see comment above about errors! ]
%D A000019 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 A000019 A. Hulpke, Konstruktion transitiver Permutationsgruppen, Dissertation, 
               RWTH Aachen, 1996.
%D A000019 A. Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 
               39 (2005), 1-30.
%D A000019 M. W. Short, The Primitive Soluble Permutation Groups of Degree less 
               than 256, LNM 1519, 1992, Springer
%D A000019 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 A000019 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000019 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000019 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 A000019 N. J. A. Sloane, <a href="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 A000019 A. Hulpke, <a href="http://www.math.colostate.edu/~hulpke/smalldeg.html">
               Transitive groups of small degree</a>
%H A000019 <a href="Sindx_Gre.html#groups">Index entries for sequences related to 
               groups</a>
%H A000019 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%o A000019 (GAP) List([2..2499],NrPrimitiveGroups);
%o A000019 (MAGMA) [NumberOfPrimitiveGroups(i) : i in [1..999]];
%Y A000019 Cf. A000001, A023675, A023676, A000637, A000638, A002106, A005432, A001493.
%Y A000019 Sequence in context: A112923 A098366 A162200 this_sequence A081177 A007281 
               A101085
%Y A000019 Adjacent sequences: A000016 A000017 A000018 this_sequence A000020 A000021 
               A000022
%K A000019 nonn,core,nice
%O A000019 1,3
%A A000019 N. J. A. Sloane (njas(AT)research.att.com).
%E A000019 More terms and additional references from Alexander Hulpke (Alexander.Hulpke(AT)Math.RWTH-Aachen.DE)

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