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

In: Forum of Mathematics, Pi, Vol. 8, e10, 26.05.2020, p. 1-26.

Research output: Contribution to journalArticle




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
Publication statusPublished - 26 May 2020
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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