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POSITIVE LAWS ON LARGE SETS OF GENERATORS: COUNTEREXAMPLES FOR INFINITELY GENERATED GROUPS

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 April 2011

CRISTINA ACCIARRI  and
GUSTAVO A. FERNÁNDEZ-ALCOBER
CRISTINA ACCIARRI
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università degli Studi dell’Aquila, I-67010 Coppito, L’Aquila, Italy (email: acciarricristina@yahoo.it)
GUSTAVO A. FERNÁNDEZ-ALCOBER*
Affiliation:
Matematika Saila, Euskal Herriko Unibertsitatea, 48080 Bilbao, Spain (email: gustavo.fernandez@ehu.es)
*
✉For correspondence; e-mail: gustavo.fernandez@ehu.es
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Abstract

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Shumyatsky and the second author proved that if G is a finitely generated residually finite p-group satisfying a law, then, for almost all primes p, the fact that a normal and commutator-closed set of generators satisfies a positive law implies that the whole of G also satisfies a (possibly different) positive law. In this paper, we construct a counterexample showing that the hypothesis of finite generation of the group G cannot be dispensed with.

Keywords

positive lawsresidually finite p-groups

MSC classification

Secondary: 20E99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 3 , December 2010 , pp. 289 - 296
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The authors are supported by the Spanish government, grant MTM2008-06680-C02-02, partly with FEDER funds, and by the Basque government, grants IT-252-07 and IT-460-10. The first author is also supported by a grant of the University of L’Aquila.

References

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