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Bulletin of the London Mathematical Society Advance Access published online on April 1, 2008
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdn007
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© 2008 London Mathematical Society

On the classification of prime-power groups by coclass

Bettina Eick

Institut Computational Mathematics
Universität Braunschweig
38106 Braunschweig
Germany

Charles Leedham-Green

School of Mathematical Sciences
Queen Mary University
London
E1 4NS
United Kingdom
C.R.Leedham-Green@qmul.ac.uk

Received 26 January 2007. Revision received 26 October 2007.

By giving a constructive proof of Conjecture P of Newman and O’Brien, we reduce the classification of certain p-groups of coclass r to a finite calculation. For the case p=2 we show that all 2-groups of coclass r can be classified by finitely many parametrised presentations. A non-constructive proof of Conjecture P was given by du Sautoy, using the theory of zeta functions. Our constructive proof uses homological algebra. It yields more precise results and detailed structure theorems for the p-groups under consideration.

2000 Mathematics Subject Classification 20D15, 20E22, 20J05.


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