A180042 The possible orders of cyclic groups that can be realized as holonomy groups of crystallographic groups in dimension 7.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, 30

Offset

1,2

Comments

In Lutowski's article the CARAT system is used to calculate a list of all isomorphism classes of 7-dimensional Bieberbach groups with cyclic holonomy group. The final list of 316 groups is presented on the undated link by the same author.

Sorted union of first floor(7/2)+1 = 4 rows of A080738. - Andrey Zabolotskiy, Jul 10 2017

Links

Table of n, a(n) for n=1..17.

H. Hiller, The Crystallographic Restriction in Higher Dimensions, Acta Cryst. (1985), A41, 541-544.

Rafal Lutowski, Seven dimensional flat manifolds with a cyclic holonomy group.

R. Lutowski, A list of 7-dimensional Bieberbach groups with cyclic holonomy, Jan 13, 2011.

W. Plesken and T. Schulz, The CARAT Homepage

W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]

W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]

Crossrefs

Sequence in context: A030477 A178859 A165412 * A096868 A266351 A206718

Adjacent sequences: A180039 A180040 A180041 * A180043 A180044 A180045

Keyword

nonn,fini,full

Author

Jonathan Vos Post, Jan 14 2011

Status

approved