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

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

2011-08-02

arxiv.org/abs/1108.0692v1

J. Aust. Math. Soc. vol. 89 (2010), 289-296

Mathematics

Group Theory

Scientific paper

10.1017/S1446788711001145

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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