cp's OEIS Frontend

A000019 Number of primitive permutation groups of degree n.

%I A000019 M0346 N0130 #73 May 31 2023 04:40:18
%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,
%U A000019 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 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_, 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 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 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. Theißen, 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 Vaclav Kotesovec, <a href="/A000019/b000019.txt">Table of n, a(n) for n = 1..4095</a>, computed using the Magma command shown below (terms 1..2499 from N. J. A. Sloane, computed using the GAP command shown below, which uses the results of Colva M. Roney-Dougal, a(1575) corrected).
%H A000019 Soleyman Askary, Nader Biranvand, and Farrokh Shirjian, <a href="https://doi.org/10.1007/s12215-023-00903-6">New constructions of orbit codes based on imprimitive wreath products and wreathed tensor products</a>, Rend. Circ. Mat. Palermo Ser. II (2023).
%H A000019 J. D. Dixon and B. Mortimer, <a href="http://dx.doi.org/10.1017/S0305004100064793">The primitive permutation groups of degree less than 1000</a>, Math. Proc. Cambridge Philos. Soc., 103, 213-238, 1988 [But see comment above about errors! ]
%H A000019 D. Holt, <a href="/A000019/a000019_1.pdf">Enumerating subgroups of the symmetric group</a>, in Computational Group Theory and the Theory of Groups, II, edited by L.-C. Kappe, A. Magidin and R. Morse. AMS Contemporary Mathematics book series, vol. 511, pp. 33-37. [Annotated copy]
%H A000019 A. Hulpke, <a href="http://www.math.colostate.edu/~hulpke/smalldeg.html">Transitive groups of small degree</a>
%H A000019 A. Hulpke, <a href="https://doi.org/10.1016/j.jsc.2004.08.002">Constructing transitive permutation groups</a>, J. Symbolic Comput. 39 (2005), 1-30.
%H A000019 J. Labelle and Y. N. Yeh, <a href="http://dx.doi.org/10.1016/0097-3165(89)90019-8">The relation between Burnside rings and combinatorial species</a>, J. Combin. Theory, A 50 (1989), 269-284. See page 280.
%H A000019 C. C. Sims, <a href="/A000019/a000019.pdf">Letter to N. J. A. Sloane (no date)</a>
%H A000019 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%H A000019 <a href="/index/Cor#core">Index entries for "core" sequences</a>
%o A000019 (GAP) List([2..2499],NrPrimitiveGroups);
%o A000019 (Magma) [NumberOfPrimitiveGroups(i) : i in [1..4095]];
%Y A000019 Cf. A000001, A023675, A023676, A000638, A002106, A005432, A000637.
%K A000019 nonn,core,nice
%O A000019 1,3
%A A000019 _N. J. A. Sloane_
%E A000019 More terms and additional references from _Alexander Hulpke_