|
Search: id:A000019
|
|
|
| A000019 |
|
Number of primitive permutation groups of degree n.
(Formerly M0346 N0130)
|
|
+0
15
|
|
| 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, 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, 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
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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
There is an error at n=574 in the Dixon-Mortimer paper. - Colva M. Roney-Dougal.
|
|
REFERENCES
|
CRC Handbook of Combinatorial Designs, 1996, pp. 595ff.
A. Hulpke, Konstruktion transitiver Permutationsgruppen, Dissertation, RWTH Aachen, 1996.
A. Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 39 (2005), 1-30.
M. W. Short, The Primitive Soluble Permutation Groups of Degree less than 256, LNM 1519, 1992, Springer
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.
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! ]
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! ]
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.
|
|
LINKS
|
N. J. A. Sloane, Table of n, a(n) for n=1..2499 [Computed using the GAP command shown below, which uses the results of Colva M. Roney-Dougal]
A. Hulpke, Transitive groups of small degree
Index entries for sequences related to groups
Index entries for "core" sequences
|
|
PROGRAM
|
(GAP) List([2..2499], NrPrimitiveGroups);
(MAGMA) [NumberOfPrimitiveGroups(i) : i in [1..999]];
|
|
CROSSREFS
|
Cf. A000001, A023675, A023676, A000637, A000638, A002106, A005432, A001493.
Sequence in context: A128971 A112923 A098366 this_sequence A081177 A007281 A101085
Adjacent sequences: A000016 A000017 A000018 this_sequence A000020 A000021 A000022
|
|
KEYWORD
|
nonn,core,nice
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms and additional references from Alexander Hulpke (Alexander.Hulpke(AT)Math.RWTH-Aachen.DE)
|
|
|
Search completed in 0.002 seconds
|
