Some collineations in projective planes induced by net collineations
Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineati...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Artzy, R. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1971 |
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| Schlagwörter: |
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| Anmerkung: |
© Birkhäuser Verlag 1971 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of geometry - Birkhäuser-Verlag, 1971, 1(1971), 2 vom: Sept., Seite 113-116 |
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| Übergeordnetes Werk: |
volume:1 ; year:1971 ; number:2 ; month:09 ; pages:113-116 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF02150265 |
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| Katalog-ID: |
OLC2069409899 |
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| 520 | |a Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. | ||
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10.1007/BF02150265 doi (DE-627)OLC2069409899 (DE-He213)BF02150265-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Artzy, R. verfasserin aut Some collineations in projective planes induced by net collineations 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1971 Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. Projective Plane Additional Requirement Translation Plane Line Pencil Multiplicative Loop Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 1(1971), 2 vom: Sept., Seite 113-116 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:1 year:1971 number:2 month:09 pages:113-116 https://doi.org/10.1007/BF02150265 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 AR 1 1971 2 09 113-116 |
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10.1007/BF02150265 doi (DE-627)OLC2069409899 (DE-He213)BF02150265-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Artzy, R. verfasserin aut Some collineations in projective planes induced by net collineations 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1971 Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. Projective Plane Additional Requirement Translation Plane Line Pencil Multiplicative Loop Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 1(1971), 2 vom: Sept., Seite 113-116 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:1 year:1971 number:2 month:09 pages:113-116 https://doi.org/10.1007/BF02150265 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 AR 1 1971 2 09 113-116 |
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10.1007/BF02150265 doi (DE-627)OLC2069409899 (DE-He213)BF02150265-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Artzy, R. verfasserin aut Some collineations in projective planes induced by net collineations 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1971 Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. Projective Plane Additional Requirement Translation Plane Line Pencil Multiplicative Loop Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 1(1971), 2 vom: Sept., Seite 113-116 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:1 year:1971 number:2 month:09 pages:113-116 https://doi.org/10.1007/BF02150265 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 AR 1 1971 2 09 113-116 |
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10.1007/BF02150265 doi (DE-627)OLC2069409899 (DE-He213)BF02150265-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Artzy, R. verfasserin aut Some collineations in projective planes induced by net collineations 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1971 Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. Projective Plane Additional Requirement Translation Plane Line Pencil Multiplicative Loop Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 1(1971), 2 vom: Sept., Seite 113-116 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:1 year:1971 number:2 month:09 pages:113-116 https://doi.org/10.1007/BF02150265 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 AR 1 1971 2 09 113-116 |
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10.1007/BF02150265 doi (DE-627)OLC2069409899 (DE-He213)BF02150265-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Artzy, R. verfasserin aut Some collineations in projective planes induced by net collineations 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag 1971 Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. Projective Plane Additional Requirement Translation Plane Line Pencil Multiplicative Loop Enthalten in Journal of geometry Birkhäuser-Verlag, 1971 1(1971), 2 vom: Sept., Seite 113-116 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:1 year:1971 number:2 month:09 pages:113-116 https://doi.org/10.1007/BF02150265 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_30 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2012 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4316 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4325 AR 1 1971 2 09 113-116 |
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Some collineations in projective planes induced by net collineations |
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Some collineations in projective planes induced by net collineations |
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Artzy, R. |
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Journal of geometry |
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1971 |
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Artzy, R. |
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Artzy, R. |
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10.1007/BF02150265 |
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510 |
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some collineations in projective planes induced by net collineations |
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Some collineations in projective planes induced by net collineations |
| abstract |
Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. © Birkhäuser Verlag 1971 |
| abstractGer |
Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. © Birkhäuser Verlag 1971 |
| abstract_unstemmed |
Abstract When in a 3-net the three line pencils are permuted, then with some additional requirements the net is mapped onto itself in a way which also induces a map of a coordinatizing loop ($ Q^{*} $), onto another, “isostrophic” loop ($ Q^{*} $, Ø). Every identity ab = aØb induces a net collineation and, simultaneously, a loop law. This procedure is used for finding collineations of a translation plane such that their existence is a necessary and sufficient condition for the validity of some laws in the multiplicative loop of a coordinatizing quasifield. Proofs can be found in [1, 2, 3]. © Birkhäuser Verlag 1971 |
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Some collineations in projective planes induced by net collineations |
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