On the commutator subgroup of a nonconnected central group

Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Herfort, Wolfgang [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	1978

Schlagwörter:	Compact Group Central Group Commutator Subgroup

Systematik:	SA 7170 SA 7170

Anmerkung:	© Springer-Verlag 1978

Übergeordnetes Werk:	Enthalten in: Monatshefte für Mathematik - Springer-Verlag, 1948, 85(1978), 1 vom: März, Seite 49-51
Übergeordnetes Werk:	volume:85 ; year:1978 ; number:1 ; month:03 ; pages:49-51

Links:	Volltext

DOI / URN:	10.1007/BF01300960

Katalog-ID:	OLC2059489075

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allfields	10.1007/BF01300960 doi (DE-627)OLC2059489075 (DE-He213)BF01300960-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 7170 VZ rvk SA 7170 VZ rvk Herfort, Wolfgang verfasserin aut On the commutator subgroup of a nonconnected central group 1978 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1978 Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. Compact Group Central Group Commutator Subgroup Enthalten in Monatshefte für Mathematik Springer-Verlag, 1948 85(1978), 1 vom: März, Seite 49-51 (DE-627)129492191 (DE-600)206474-1 (DE-576)014887657 0026-9255 nnns volume:85 year:1978 number:1 month:03 pages:49-51 https://doi.org/10.1007/BF01300960 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2012 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4029 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 7170 SA 7170 AR 85 1978 1 03 49-51
spelling	10.1007/BF01300960 doi (DE-627)OLC2059489075 (DE-He213)BF01300960-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 7170 VZ rvk SA 7170 VZ rvk Herfort, Wolfgang verfasserin aut On the commutator subgroup of a nonconnected central group 1978 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1978 Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. Compact Group Central Group Commutator Subgroup Enthalten in Monatshefte für Mathematik Springer-Verlag, 1948 85(1978), 1 vom: März, Seite 49-51 (DE-627)129492191 (DE-600)206474-1 (DE-576)014887657 0026-9255 nnns volume:85 year:1978 number:1 month:03 pages:49-51 https://doi.org/10.1007/BF01300960 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2012 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4029 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 7170 SA 7170 AR 85 1978 1 03 49-51
allfields_unstemmed	10.1007/BF01300960 doi (DE-627)OLC2059489075 (DE-He213)BF01300960-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 7170 VZ rvk SA 7170 VZ rvk Herfort, Wolfgang verfasserin aut On the commutator subgroup of a nonconnected central group 1978 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1978 Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. Compact Group Central Group Commutator Subgroup Enthalten in Monatshefte für Mathematik Springer-Verlag, 1948 85(1978), 1 vom: März, Seite 49-51 (DE-627)129492191 (DE-600)206474-1 (DE-576)014887657 0026-9255 nnns volume:85 year:1978 number:1 month:03 pages:49-51 https://doi.org/10.1007/BF01300960 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2012 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4029 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 7170 SA 7170 AR 85 1978 1 03 49-51
allfieldsGer	10.1007/BF01300960 doi (DE-627)OLC2059489075 (DE-He213)BF01300960-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 7170 VZ rvk SA 7170 VZ rvk Herfort, Wolfgang verfasserin aut On the commutator subgroup of a nonconnected central group 1978 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1978 Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. Compact Group Central Group Commutator Subgroup Enthalten in Monatshefte für Mathematik Springer-Verlag, 1948 85(1978), 1 vom: März, Seite 49-51 (DE-627)129492191 (DE-600)206474-1 (DE-576)014887657 0026-9255 nnns volume:85 year:1978 number:1 month:03 pages:49-51 https://doi.org/10.1007/BF01300960 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2012 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4029 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 7170 SA 7170 AR 85 1978 1 03 49-51
allfieldsSound	10.1007/BF01300960 doi (DE-627)OLC2059489075 (DE-He213)BF01300960-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn SA 7170 VZ rvk SA 7170 VZ rvk Herfort, Wolfgang verfasserin aut On the commutator subgroup of a nonconnected central group 1978 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1978 Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. Compact Group Central Group Commutator Subgroup Enthalten in Monatshefte für Mathematik Springer-Verlag, 1948 85(1978), 1 vom: März, Seite 49-51 (DE-627)129492191 (DE-600)206474-1 (DE-576)014887657 0026-9255 nnns volume:85 year:1978 number:1 month:03 pages:49-51 https://doi.org/10.1007/BF01300960 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_60 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2012 GBV_ILN_2020 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4029 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 SA 7170 SA 7170 AR 85 1978 1 03 49-51
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author	Herfort, Wolfgang
spellingShingle	Herfort, Wolfgang ddc 510 ssgn 17,1 rvk SA 7170 misc Compact Group misc Central Group misc Commutator Subgroup On the commutator subgroup of a nonconnected central group
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topic_title	510 VZ 17,1 ssgn SA 7170 VZ rvk On the commutator subgroup of a nonconnected central group Compact Group Central Group Commutator Subgroup
topic	ddc 510 ssgn 17,1 rvk SA 7170 misc Compact Group misc Central Group misc Commutator Subgroup
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title	On the commutator subgroup of a nonconnected central group
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title_full	On the commutator subgroup of a nonconnected central group
author_sort	Herfort, Wolfgang
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title_sort	on the commutator subgroup of a nonconnected central group
title_auth	On the commutator subgroup of a nonconnected central group
abstract	Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. © Springer-Verlag 1978
abstractGer	Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. © Springer-Verlag 1978
abstract_unstemmed	Abstract In this paperG denotes a central topologicalT2-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG′; in general (G′)− is compact ([3]), but not necessarilyG′ ([7]). If in additionG is a Lie group or ifG is connected,G′ is compact ([6], [5]). The purpose of this paper is to show, that if the componentG0 of the identity is open,G′ must be compact, and to give an example of a compact group with (G/G0)′ compact, whileG′ is not compact. © Springer-Verlag 1978
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title_short	On the commutator subgroup of a nonconnected central group
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