On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon
Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of...
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| Autor*in: |
Bishnoi, Anurag [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer International Publishing 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of combinatorics - Springer International Publishing, 1997, 20(2016), 3 vom: 07. Mai, Seite 433-452 |
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| Übergeordnetes Werk: |
volume:20 ; year:2016 ; number:3 ; day:07 ; month:05 ; pages:433-452 |
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| DOI / URN: |
10.1007/s00026-016-0315-z |
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| 520 | |a Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). | ||
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10.1007/s00026-016-0315-z doi (DE-627)OLC2061535941 (DE-He213)s00026-016-0315-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bishnoi, Anurag verfasserin aut On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). generalized hexagon near hexagon valuation De Bruyn, Bart aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 20(2016), 3 vom: 07. Mai, Seite 433-452 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:20 year:2016 number:3 day:07 month:05 pages:433-452 https://doi.org/10.1007/s00026-016-0315-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2088 AR 20 2016 3 07 05 433-452 |
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10.1007/s00026-016-0315-z doi (DE-627)OLC2061535941 (DE-He213)s00026-016-0315-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bishnoi, Anurag verfasserin aut On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). generalized hexagon near hexagon valuation De Bruyn, Bart aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 20(2016), 3 vom: 07. Mai, Seite 433-452 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:20 year:2016 number:3 day:07 month:05 pages:433-452 https://doi.org/10.1007/s00026-016-0315-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2088 AR 20 2016 3 07 05 433-452 |
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10.1007/s00026-016-0315-z doi (DE-627)OLC2061535941 (DE-He213)s00026-016-0315-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bishnoi, Anurag verfasserin aut On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). generalized hexagon near hexagon valuation De Bruyn, Bart aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 20(2016), 3 vom: 07. Mai, Seite 433-452 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:20 year:2016 number:3 day:07 month:05 pages:433-452 https://doi.org/10.1007/s00026-016-0315-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2088 AR 20 2016 3 07 05 433-452 |
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10.1007/s00026-016-0315-z doi (DE-627)OLC2061535941 (DE-He213)s00026-016-0315-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bishnoi, Anurag verfasserin aut On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). generalized hexagon near hexagon valuation De Bruyn, Bart aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 20(2016), 3 vom: 07. Mai, Seite 433-452 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:20 year:2016 number:3 day:07 month:05 pages:433-452 https://doi.org/10.1007/s00026-016-0315-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2088 AR 20 2016 3 07 05 433-452 |
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10.1007/s00026-016-0315-z doi (DE-627)OLC2061535941 (DE-He213)s00026-016-0315-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Bishnoi, Anurag verfasserin aut On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). generalized hexagon near hexagon valuation De Bruyn, Bart aut Enthalten in Annals of combinatorics Springer International Publishing, 1997 20(2016), 3 vom: 07. Mai, Seite 433-452 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:20 year:2016 number:3 day:07 month:05 pages:433-452 https://doi.org/10.1007/s00026-016-0315-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2088 AR 20 2016 3 07 05 433-452 |
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Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). © Springer International Publishing 2016 |
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Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). © Springer International Publishing 2016 |
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Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. We show here that no semi–finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its point–line dual HD(2). In fact, the employed techniques allow us to prove a stronger result. We show that every near hexagon $${\mathcal{S}}$$ of order (2, t) which contains a generalized hexagon H of order 2 as an isometrically embedded subgeometry must be finite. Moreover, if $${H \cong H^{D}}$$(2) then $${\mathcal{S}}$$ must also be a generalized hexagon, and consequently isomorphic to either HD(2) or the dual twisted triality hexagon T(2, 8). © Springer International Publishing 2016 |
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| doi_str |
10.1007/s00026-016-0315-z |
| up_date |
2024-07-04T03:49:23.901Z |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2061535941</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230323113644.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00026-016-0315-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2061535941</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00026-016-0315-z-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bishnoi, Anurag</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</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 International Publishing 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi–finite thick generalized polygons. 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