On FC-central extensions of groups of intermediate growth

2020/01/21 by Tianyi Zheng, Zheng, Tianyi
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2001.07814

openalex publication_date 2020/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ℤ^∞; and the other provides groups with prescribed oscillating intermediate growth functions.

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