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arXiv · 1108.0692

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

C. Acciarri·G. A. Fernández-Alcober
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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, 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.

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C. Acciarri, G. A. Fernández-Alcober. 2011-08-02. Positive laws on large sets of generators: counterexamples for infinitely generated groups. https://doi.org/10.1017/s1446788711001145

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