Pro-p groups with linear subgroup growth

Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigat...
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Gespeichert in:

Autor*in:	Klopsch, Benjamin [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2003

Schlagwörter:	Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2003

Übergeordnetes Werk:	Enthalten in: Mathematische Zeitschrift - Springer-Verlag, 1918, 245(2003), 2 vom: 16. Aug., Seite 335-370
Übergeordnetes Werk:	volume:245 ; year:2003 ; number:2 ; day:16 ; month:08 ; pages:335-370

Links:	Volltext

DOI / URN:	10.1007/s00209-003-0548-5

Katalog-ID:	OLC2039723382

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allfields	10.1007/s00209-003-0548-5 doi (DE-627)OLC2039723382 (DE-He213)s00209-003-0548-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Klopsch, Benjamin verfasserin aut Pro-p groups with linear subgroup growth 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup Enthalten in Mathematische Zeitschrift Springer-Verlag, 1918 245(2003), 2 vom: 16. Aug., Seite 335-370 (DE-627)129474193 (DE-600)203014-7 (DE-576)014852047 0025-5874 nnns volume:245 year:2003 number:2 day:16 month:08 pages:335-370 https://doi.org/10.1007/s00209-003-0548-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 245 2003 2 16 08 335-370
spelling	10.1007/s00209-003-0548-5 doi (DE-627)OLC2039723382 (DE-He213)s00209-003-0548-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Klopsch, Benjamin verfasserin aut Pro-p groups with linear subgroup growth 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup Enthalten in Mathematische Zeitschrift Springer-Verlag, 1918 245(2003), 2 vom: 16. Aug., Seite 335-370 (DE-627)129474193 (DE-600)203014-7 (DE-576)014852047 0025-5874 nnns volume:245 year:2003 number:2 day:16 month:08 pages:335-370 https://doi.org/10.1007/s00209-003-0548-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 245 2003 2 16 08 335-370
allfields_unstemmed	10.1007/s00209-003-0548-5 doi (DE-627)OLC2039723382 (DE-He213)s00209-003-0548-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Klopsch, Benjamin verfasserin aut Pro-p groups with linear subgroup growth 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup Enthalten in Mathematische Zeitschrift Springer-Verlag, 1918 245(2003), 2 vom: 16. Aug., Seite 335-370 (DE-627)129474193 (DE-600)203014-7 (DE-576)014852047 0025-5874 nnns volume:245 year:2003 number:2 day:16 month:08 pages:335-370 https://doi.org/10.1007/s00209-003-0548-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 245 2003 2 16 08 335-370
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allfieldsSound	10.1007/s00209-003-0548-5 doi (DE-627)OLC2039723382 (DE-He213)s00209-003-0548-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Klopsch, Benjamin verfasserin aut Pro-p groups with linear subgroup growth 2003 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2003 Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup Enthalten in Mathematische Zeitschrift Springer-Verlag, 1918 245(2003), 2 vom: 16. Aug., Seite 335-370 (DE-627)129474193 (DE-600)203014-7 (DE-576)014852047 0025-5874 nnns volume:245 year:2003 number:2 day:16 month:08 pages:335-370 https://doi.org/10.1007/s00209-003-0548-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2030 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4320 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 245 2003 2 16 08 335-370
language	English
source	Enthalten in Mathematische Zeitschrift 245(2003), 2 vom: 16. Aug., Seite 335-370 volume:245 year:2003 number:2 day:16 month:08 pages:335-370
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topic_facet	Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup
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author	Klopsch, Benjamin
spellingShingle	Klopsch, Benjamin ddc 510 ssgn 17,1 misc Natural Number misc Subgroup Growth misc Polynomial Subgroup misc Polynomial Subgroup Growth misc Linear Subgroup Pro-p groups with linear subgroup growth
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topic_title	510 VZ 17,1 ssgn Pro-p groups with linear subgroup growth Natural Number Subgroup Growth Polynomial Subgroup Polynomial Subgroup Growth Linear Subgroup
topic	ddc 510 ssgn 17,1 misc Natural Number misc Subgroup Growth misc Polynomial Subgroup misc Polynomial Subgroup Growth misc Linear Subgroup
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title	Pro-p groups with linear subgroup growth
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title_full	Pro-p groups with linear subgroup growth
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title_sort	pro-p groups with linear subgroup growth
title_auth	Pro-p groups with linear subgroup growth
abstract	Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. © Springer-Verlag Berlin Heidelberg 2003
abstractGer	Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. © Springer-Verlag Berlin Heidelberg 2003
abstract_unstemmed	Abstract. Let G be a finitely generated pro-p group, and for every natural number n let sn(G) denote the number of subgroups of index at most n in G. The group G is said to have polynomial subgroup growth (PSG), if there exists α$ ℝ_{≥0} $ such that sn(G)≤nα for all nℕ. In this paper we investigate the structure of pro-p groups which have (slow) PSG. Our main result is a complete description of pro-p groups with linear subgroup growth; this solves a problem posed by Shalev [20]. © Springer-Verlag Berlin Heidelberg 2003
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title_short	Pro-p groups with linear subgroup growth
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up_date	2024-07-03T23:48:07.188Z
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