A353341 Number of 4-dimensional point groups of order n.

1, 4, 3, 11, 4, 14, 5, 29, 8, 18, 7, 41, 8, 22, 14, 56, 10, 37, 11, 51, 18, 30, 13, 100, 17, 34, 22, 60, 16, 64, 17, 98, 26, 42, 26, 101, 20, 46, 30, 112, 22, 80, 23, 80, 42, 54, 25, 189, 30, 73, 38, 91, 28, 96, 38, 133, 42, 66, 31, 170, 32, 70, 55, 167, 44

Offset

1,2

Comments

In other words, the number of (finite) subgroups of order n of the orthogonal group O(4).

References

John H. Conway and Derek A. Smith, On Quaternions and Octonions, CRC Press, 2003.

Patrick Du Val, Homographies, Quaternions and Rotations. Clarendon Press, 1964.

Links

Laith Rastanawi and Günter Rote, Table of n, a(n) for n = 1..10000

Edouard Goursat, Sur les substitutions orthogonales et les divisions régulières de l'espace, Annales scientifiques de l'E.N.S. 3e série, 6:9-102, 1889.

A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Mathematical Proceedings of the Cambridge Philosophical Society, 47(4):650-661, 1951.

Laith Rastanawi and Günter Rote, Towards a Geometric Understanding of the 4-Dimensional Point Groups, arXiv preprint arXiv:2205.04965 [math.MG], 2022.

Laith Rastanawi and Günter Rote, Sage code used to generate the sequence.

W. Threlfall and H. Seifert, Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes, Math. Annalen, 104:1-70, 1931.

W. Threlfall and H. Seifert, Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes (Schluß), Math. Annalen, 107:543-586, 1933.

Crossrefs

Cf. A354046.

Sequence in context: A222510 A100492 A072183 * A346614 A370631 A370630

Adjacent sequences: A353338 A353339 A353340 * A353342 A353343 A353344

Keyword

nonn

Author

Laith Rastanawi and Günter Rote, May 16 2022

Status

approved