A000637 Number of fixed-point-free permutation groups of degree n.

1, 0, 1, 2, 7, 8, 37, 40, 200, 258, 1039, 1501, 7629, 10109, 54322, 83975, 527036, 780193, 5808293

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice

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

• 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

Crossrefs

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

Cf. A000019, A002106. Unlabeled version of A116693.

Formula

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

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