Branch groups, orbit growth, and new subgroup growth types for pro-p groups. / Barnea, Yiftach; Schlage-Puchta, J.C.

In: ArXiv.org, 17.10.2017.

Research output: Contribution to journalArticle

In preparation

Abstract

We first show that a class of pro-$p$ branch groups including the Grigorchuk group and the Gupta-Sidki groups all have subgroup growth type $n^{\log n}$. We then introduce the notion of orbit growth and use it to construct extensions of the Grigorchuk group and the Gupta-Sidki groups. We compute the subgroup growth type of these extensions and deduce that all functions between $n^{(\log n)^2}$ and $e^n$ occur as the subgroup growth type of a pro-$p$ group, thus, giving almost complete answer to a question raised by Lubotzky and Segal.
Original languageEnglish
JournalArXiv.org
Publication statusIn preparation - 17 Oct 2017
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 28843143