论文标题
在中间生长组的FC中心扩展
On FC-central extensions of groups of intermediate growth
论文作者
论文摘要
结果表明，FC中心扩展保留了亚指数体积的增长。 Erschler和Kassabov-Pak的作品中提供了大量的Grigorchuk组的FC中心扩展。我们表明，在这些示例中，亚组可分离性保留了。我们介绍了Grigorchuk Group的两个新系列。一个集合给出了具有同构为$ \ mathbb {z}^{\ infty} $的中心增长组的第一个示例;另一个为基团提供了规定的振荡中间生长功能。
It is shown that FC-central extensions retain sub-exponential volume growth. A large collection of FC-central extensions of the first Grigorchuk group is provided by the constructions in the works of Erschler and Kassabov-Pak. We show that in these examples subgroup separability is preserved. We introduce two new collections of extensions of the Grigorchuk group. One collection gives first examples of intermediate growth groups with centers isomorphic to $\mathbb{Z}^{\infty}$; and the other provides groups with prescribed oscillating intermediate growth functions.
