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DETERMINATION OF THE UNISERIAL SPACE GROUPS WITH A GIVEN COCLASS

Published online by Cambridge University Press:  24 May 2005

BETTINA EICK
BETTINA EICK
Affiliation:
Institut Computational Mathematics, Universität Braunschweig, 38106 Braunschweig, Germany
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Abstract

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.

Keywords

20-0420C1120E2220J05
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 622 - 642
Copyright
The London Mathematical Society 2005

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