Branch groups, orbit growth, and subgroup growth types for pro-p groups

Yiftach Barnea, J-C Schlage-Puchta

Research output: Contribution to journalArticle

Abstract

In their book Subgroup Growth, Lubotzky and Segal asked what are the possible types of subgroup growth of pro-$p$ group? In this paper, we construct certain extensions of the Grigorchuk group and the Gupta-Sidki groups which have all possible types of subgroup growth between $n^{(\log n)^2}$ and $e^n$. Thus, we give an almost complete answer to Lubotzky and Segal's question. In addition, we show that a class of pro-$p$ branch groups, including the Grigorchuk group and the Gupta-Sidki groups, all have subgroup growth type $n^{\log n}$.
Original languageEnglish
Article numbere10
Pages (from-to)1-26
Number of pages26
JournalForum of Mathematics, Pi
Volume8
DOIs
Publication statusPublished - 26 May 2020

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