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Enumerating p-Groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Bettina Eick  and
E. A. O'Brien
Bettina Eick
Affiliation:
Fachbereich Mathematik Universität Kassel Heinrich-Plett-Str. 40 34132 Kassel Germany e-mail: eick@mathematik.uni-kassel.de
E. A. O'Brien
Affiliation:
Department of Mathmatics University of Auckland Private Bag 92019 Auckland New Zealand e-mail: obrien@math.auckland.ac.nz
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Abstract

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We present a new algorithm which uses a cohomological approach to determine the groups of order pn, where p is a prime. We develop two methods to enumerate p-groups using the Cauchy-Frobenius Lemma. As an application we show that there are 10 494213 groups of order 29.

1991 Mathematics subject classification (Amer. Math. Soc.): primary 20D15.

Keywords

p-groupsenumerationcohomologyCauchy-Frobenius lemma.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 2 , October 1999 , pp. 191 - 205
Copyright
Copyright © Australian Mathematical Society 1999

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