生成元大集上的正律：无限生成群的反例
Positive laws on large sets of generators: counterexamples for infinitely generated groups
摘要：
Shumyatsky和第二作者证明了，如果G是一个生成的剩余有限p-群满足一个定律，那么，对于几乎所有的素数，一个正常的和交换子-闭集的生成元满足一个正定律的事实意味着整个G也满足一个（可能不同的）正定律。本文构造了一个反例，说明群G的有限生成假设是不能抛弃的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
