标题： 有限性性质的剩余自由群 显示英文标题

标题： Profinite properties of residually free groups

摘要： 亨利·威尔顿分类了当一个素三维流形$M$具有剩余自由基本群$\pi_1 M$的情况。 我们证明了群$\pi_1 M\times \mathbb Z^n$在有限生成的剩余自由群中是完全有限刚性的。 我们还建立了剩余自由群类的其他完全有限不变量，例如一致性与子群可分性。 在我们的证明过程中，我们推广了威尔顿和扎列斯基关于完全有限识别群的中心扩张何时分裂的一个引理。 显示英文摘要

摘要： Henry Wilton classified when a prime three-manifold $M$ has a residually free fundamental group $\pi_1 M$. We prove that the groups $\pi_1 M\times \mathbb Z^n$ are profinitely rigid within finitely generated residually free groups. We also establish other profinite invariants of the class of residually free groups such as coherence and subgroup separability. In the course of our proofs, we generalise a lemma of Wilton and Zalesskii on profinitely recognising when a central extension of groups splits.