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

Author

Jonathan Vos Post, Jan 14 2011

Keywords

• nonn
• fini
• full

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

• 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]