Premium
Determination of the Uniserial Space Groups with a given Coclass
Author(s) -
Eick Bettina
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006332
Subject(s) - isomorphism (crystallography) , space (punctuation) , prime (order theory) , group (periodic table) , space group , pure mathematics , mathematics , combinatorics , computer science , physics , chemistry , crystallography , crystal structure , x ray crystallography , diffraction , optics , operating system , quantum mechanics
The uniserial p ‐adic space groups of coclass r play a central role in the classification of the finite p ‐groups of coclass r . A practical algorithm to determine up to isomorphism the uniserial p ‐adic space groups of coclass r , where p is an odd prime, is described. As an application, these groups are constructed or counted for some values on p and r . For example, it is observed that there are 137 299 953 383 uniserial 3‐adic space groups of coclass 4.