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A000637 Number of fixed-point-free permutation groups of degree n.
(Formerly M1730 N0685)
12
1, 0, 1, 2, 7, 8, 37, 40, 200, 258, 1039, 1501, 7629, 10109, 54322, 83975, 527036, 780193, 5808293 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(1) = 0 since the trivial group of degree 1 has a fixed point. One could also argue that one should set a(1) = 1 by convention.

REFERENCES

G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra, 11 (1983), 863-911.

D. Holt, Enumerating subgroups of the symmetric group. 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.

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

A. Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 39 (2005), 1-30.

A. Hulpke, Constructing Transitive Permutation Groups, in preparation

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.

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

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

LINKS

Table of n, a(n) for n=0..18.

G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra, 11 (1983), 863-911. [Annotated scanned copy]

D. Holt, Enumerating subgroups of the symmetric group, 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]

A. Hulpke, Transitive groups of small degree

A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 1027-1079.

A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 1027-1079. [Annotated scan of page 1069 only]

C. C. Sims, Letter to N. J. A. Sloane (no date)

Index entries for sequences related to groups

FORMULA

a(n) = A000638(n)-A000638(n-1). - Christian G. Bower, Feb 23 2006

CROSSREFS

Cf. A000001, A000019, A000638, A002106, A005432, A005226.

Cf. A000019, A002106. Unlabeled version of A116693.

Sequence in context: A081700 A093795 A001493 * A250715 A198322 A222134

Adjacent sequences:  A000634 A000635 A000636 * A000638 A000639 A000640

KEYWORD

nonn,hard,more,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Alexander Hulpke

a(2) and a(10) corrected, a(11) and a(12) added by Christian G. Bower, Feb 23 2006

Terms a(13)-a(18) were computed by Derek Holt and contributed by Alexander Hulpke. Jul 30 2010, who comments that he has verified the terms up through a(16).

Edited by N. J. A. Sloane, Jul 30 2010, at the suggestion of Michael Somos

STATUS

approved

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Last modified July 25 18:32 EDT 2021. Contains 346291 sequences. (Running on oeis4.)