Automorphisms of Coxeter groups of type Kn
Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any autom...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ryan, J. A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, Inc. 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Siberian mathematical journal - Kluwer Academic Publishers-Consultants Bureau, 1966, 48(2007), 2 vom: März, Seite 311-316 |
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| Übergeordnetes Werk: |
volume:48 ; year:2007 ; number:2 ; month:03 ; pages:311-316 |
| Links: |
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| DOI / URN: |
10.1007/s11202-007-0032-2 |
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OLC2033380688 |
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| 520 | |a Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). | ||
| 650 | 4 | |a Coxeter group | |
| 650 | 4 | |a graph | |
| 650 | 4 | |a automorphism | |
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10.1007/s11202-007-0032-2 doi (DE-627)OLC2033380688 (DE-He213)s11202-007-0032-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ryan, J. A. verfasserin aut Automorphisms of Coxeter groups of type Kn 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). Coxeter group graph automorphism Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 2 vom: März, Seite 311-316 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:2 month:03 pages:311-316 https://doi.org/10.1007/s11202-007-0032-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 48 2007 2 03 311-316 |
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10.1007/s11202-007-0032-2 doi (DE-627)OLC2033380688 (DE-He213)s11202-007-0032-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ryan, J. A. verfasserin aut Automorphisms of Coxeter groups of type Kn 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). Coxeter group graph automorphism Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 2 vom: März, Seite 311-316 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:2 month:03 pages:311-316 https://doi.org/10.1007/s11202-007-0032-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 48 2007 2 03 311-316 |
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10.1007/s11202-007-0032-2 doi (DE-627)OLC2033380688 (DE-He213)s11202-007-0032-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ryan, J. A. verfasserin aut Automorphisms of Coxeter groups of type Kn 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). Coxeter group graph automorphism Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 2 vom: März, Seite 311-316 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:2 month:03 pages:311-316 https://doi.org/10.1007/s11202-007-0032-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 AR 48 2007 2 03 311-316 |
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Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). © Springer Science+Business Media, Inc. 2007 |
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Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). © Springer Science+Business Media, Inc. 2007 |
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Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type Kn then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). © Springer Science+Business Media, Inc. 2007 |
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A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Automorphisms of Coxeter groups of type Kn</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2007</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, Inc. 2007</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract A Coxeter system (W, S) is said to be of type Kn if the associated Coxeter graph $ Γ_{S} $ is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by $ Γ_{S} $. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. 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