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A BOUND ON THE PRESENTATION RANK OF A FINITE GROUP

Published online by Cambridge University Press:  01 July 1997

ANDREA LUCCHINI
ANDREA LUCCHINI
Affiliation:
Dipartimento di Elettronica per l'Automazione, Università di Brescia, Via Branze, 25123 Brescia, Italy
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Abstract

Let G be a finite group, and let IG be the augmentation ideal of ℤG. We denote by d(G) the minimum number of generators for the group G, and by d(IG) the minimum number of elements of IG needed to generate IG as a G-module. The connection between d(G) and d(IG) is given by the following result due to Roggenkamp ]14&]:

formula here

where pr(G) is a non-negative integer, called the presentation rank of G, whose definition comes from the study of relation modules (see [4&] for more details).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 4 , July 1997 , pp. 389 - 394
Copyright
© The London Mathematical Society 1997

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