The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type
Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kostousov, K. V. [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), 3 vom: Mai, Seite 489-499 |
|---|---|
| Übergeordnetes Werk: |
volume:48 ; year:2007 ; number:3 ; month:05 ; pages:489-499 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11202-007-0051-z |
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OLC2033380882 |
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| 520 | |a Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. | ||
| 650 | 4 | |a vertex-primitive graph | |
| 650 | 4 | |a edge-transitive graph | |
| 650 | 4 | |a limit graph | |
| 650 | 4 | |a Cayley graph of a finite rank free abelian group | |
| 650 | 4 | |a crystallographic group | |
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10.1007/s11202-007-0051-z doi (DE-627)OLC2033380882 (DE-He213)s11202-007-0051-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kostousov, K. V. verfasserin aut The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. vertex-primitive graph edge-transitive graph limit graph Cayley graph of a finite rank free abelian group crystallographic group Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 3 vom: Mai, Seite 489-499 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:3 month:05 pages:489-499 https://doi.org/10.1007/s11202-007-0051-z 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 3 05 489-499 |
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10.1007/s11202-007-0051-z doi (DE-627)OLC2033380882 (DE-He213)s11202-007-0051-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kostousov, K. V. verfasserin aut The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. vertex-primitive graph edge-transitive graph limit graph Cayley graph of a finite rank free abelian group crystallographic group Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 3 vom: Mai, Seite 489-499 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:3 month:05 pages:489-499 https://doi.org/10.1007/s11202-007-0051-z 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 3 05 489-499 |
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10.1007/s11202-007-0051-z doi (DE-627)OLC2033380882 (DE-He213)s11202-007-0051-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kostousov, K. V. verfasserin aut The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. vertex-primitive graph edge-transitive graph limit graph Cayley graph of a finite rank free abelian group crystallographic group Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 3 vom: Mai, Seite 489-499 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:3 month:05 pages:489-499 https://doi.org/10.1007/s11202-007-0051-z 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 3 05 489-499 |
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10.1007/s11202-007-0051-z doi (DE-627)OLC2033380882 (DE-He213)s11202-007-0051-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kostousov, K. V. verfasserin aut The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. vertex-primitive graph edge-transitive graph limit graph Cayley graph of a finite rank free abelian group crystallographic group Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 3 vom: Mai, Seite 489-499 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:3 month:05 pages:489-499 https://doi.org/10.1007/s11202-007-0051-z 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 3 05 489-499 |
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10.1007/s11202-007-0051-z doi (DE-627)OLC2033380882 (DE-He213)s11202-007-0051-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kostousov, K. V. verfasserin aut The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2007 Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. vertex-primitive graph edge-transitive graph limit graph Cayley graph of a finite rank free abelian group crystallographic group Enthalten in Siberian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1966 48(2007), 3 vom: Mai, Seite 489-499 (DE-627)129553573 (DE-600)220062-4 (DE-576)015009602 0037-4466 nnns volume:48 year:2007 number:3 month:05 pages:489-499 https://doi.org/10.1007/s11202-007-0051-z 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 3 05 489-499 |
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The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type |
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Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. © Springer Science+Business Media, Inc. 2007 |
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Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. © Springer Science+Business Media, Inc. 2007 |
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Abstract We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups $ ℤ^{d} $. In this article we prove that for each d > 1 the set of Cayley graphs of $ ℤ^{d} $ presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of $ ℤ^{d} $ that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of $ ℤ^{d} $ with crystallographic groups. © Springer Science+Business Media, Inc. 2007 |
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The Cayley graphs of $ ℤ^{d} $ and the limits of vertex-primitive graphs of HA-type |
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10.1007/s11202-007-0051-z |
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