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

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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

Harvard

Barnea, Y & Schlage-Puchta, J-C 2020, 'Branch groups, orbit growth, and subgroup growth types for pro-p groups', Forum of Mathematics, Pi, vol. 8, e10, pp. 1-26. https://doi.org/10.1017/fmp.2020.8

APA

Barnea, Y., & Schlage-Puchta, J-C. (2020). Branch groups, orbit growth, and subgroup growth types for pro-p groups. Forum of Mathematics, Pi, 8, 1-26. [e10]. https://doi.org/10.1017/fmp.2020.8

Vancouver

Author

Barnea, Yiftach ; Schlage-Puchta, J-C. / Branch groups, orbit growth, and subgroup growth types for pro-p groups. In: Forum of Mathematics, Pi. 2020 ; Vol. 8. pp. 1-26.

BibTeX

@article{6e7eb43b6fa2440d8b4a308c7d5572c1,
title = "Branch groups, orbit growth, and subgroup growth types for pro-p groups",
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 $n^{\log n}$. ",
author = "Yiftach Barnea and J-C Schlage-Puchta",
year = "2020",
month = may,
day = "26",
doi = "10.1017/fmp.2020.8",
language = "English",
volume = "8",
pages = "1--26",
journal = "Forum of Mathematics, Pi",
issn = "2050-5086",

}

RIS

TY - JOUR

T1 - Branch groups, orbit growth, and subgroup growth types for pro-p groups

AU - Barnea, Yiftach

AU - Schlage-Puchta, J-C

PY - 2020/5/26

Y1 - 2020/5/26

N2 - 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 $n^{\log n}$.

AB - 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 $n^{\log n}$.

U2 - 10.1017/fmp.2020.8

DO - 10.1017/fmp.2020.8

M3 - Article

VL - 8

SP - 1

EP - 26

JO - Forum of Mathematics, Pi

JF - Forum of Mathematics, Pi

SN - 2050-5086

M1 - e10

ER -