Positive laws on large sets of generators: counterexamples for infinitely generated groups
Group Theory
2011-08-04 v1
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.
Keywords
Cite
@article{arxiv.1108.0692,
title = {Positive laws on large sets of generators: counterexamples for infinitely generated groups},
author = {C. Acciarri and G. A. Fernández-Alcober},
journal= {arXiv preprint arXiv:1108.0692},
year = {2011}
}