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.

Positive laws on large sets of generators: counterexamples for infinitely generated groups / Acciarri, C; FERNÁNDEZ-ALCOBER G., A. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - 89:03(2010), pp. 289-296. [10.1017/S1446788711001145]

Positive laws on large sets of generators: counterexamples for infinitely generated groups

ACCIARRI C;
2010-01-01

Abstract

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.
89
03
289
296
Positive laws on large sets of generators: counterexamples for infinitely generated groups / Acciarri, C; FERNÁNDEZ-ALCOBER G., A. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - 89:03(2010), pp. 289-296. [10.1017/S1446788711001145]
Acciarri, C; FERNÁNDEZ-ALCOBER G., A
File in questo prodotto:
File Dimensione Formato  
positive-laws-on-large-sets-of-generators-counterexamples-for-infinitely-generated-groups_l.pdf

Open access

Tipologia: Versione pubblicata dall'editore
Dimensione 127.69 kB
Formato Adobe PDF
127.69 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1255529
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact