Resumen de Determination of the uniserial space groups with a given coclass

Bettina Erick

• The uniserial -adic space groups of coclass play a central role in the classification of the finite -groups of coclass . A practical algorithm to determine up to isomorphism the uniserial -adic space groups of coclass , where is an odd prime, is described. As an application, these groups are constructed or counted for some values on and . For example, it is observed that there are 137 299 953 383 uniserial 3-adic space groups of coclass 4.