On triple factorizations of finite groups
Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper...
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| Autor*in: |
Alavi, S. Hassan [verfasserIn] Praeger, Cheryl E. [verfasserIn] |
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E-Artikel |
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Walter de Gruyter GmbH & Co. KG ; 2010 |
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20 |
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| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Journal of group theory - Berlin : de Gruyter, 1998, 14(2010), 3 vom: 13. Okt., Seite 341-360 |
| Übergeordnetes Werk: |
volume:14 ; year:2010 ; number:3 ; day:13 ; month:10 ; pages:341-360 ; extent:20 |
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| DOI / URN: |
10.1515/jgt.2010.052 |
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NLEJ247080896 |
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| 520 | |a Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. | ||
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10.1515/jgt.2010.052 doi artikel_Grundlieferung.pp (DE-627)NLEJ247080896 DE-627 ger DE-627 rakwb Alavi, S. Hassan verfasserin aut On triple factorizations of finite groups Walter de Gruyter GmbH & Co. KG 2010 20 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. Walter de Gruyter Online Zeitschriften Praeger, Cheryl E. verfasserin aut Enthalten in Journal of group theory Berlin : de Gruyter, 1998 14(2010), 3 vom: 13. Okt., Seite 341-360 (DE-627)NLEJ248236075 (DE-600)1492030-X 1435-4446 nnns volume:14 year:2010 number:3 day:13 month:10 pages:341-360 extent:20 https://doi.org/10.1515/jgt.2010.052 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 2010 3 13 10 341-360 20 |
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10.1515/jgt.2010.052 doi artikel_Grundlieferung.pp (DE-627)NLEJ247080896 DE-627 ger DE-627 rakwb Alavi, S. Hassan verfasserin aut On triple factorizations of finite groups Walter de Gruyter GmbH & Co. KG 2010 20 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. Walter de Gruyter Online Zeitschriften Praeger, Cheryl E. verfasserin aut Enthalten in Journal of group theory Berlin : de Gruyter, 1998 14(2010), 3 vom: 13. Okt., Seite 341-360 (DE-627)NLEJ248236075 (DE-600)1492030-X 1435-4446 nnns volume:14 year:2010 number:3 day:13 month:10 pages:341-360 extent:20 https://doi.org/10.1515/jgt.2010.052 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 2010 3 13 10 341-360 20 |
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10.1515/jgt.2010.052 doi artikel_Grundlieferung.pp (DE-627)NLEJ247080896 DE-627 ger DE-627 rakwb Alavi, S. Hassan verfasserin aut On triple factorizations of finite groups Walter de Gruyter GmbH & Co. KG 2010 20 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. Walter de Gruyter Online Zeitschriften Praeger, Cheryl E. verfasserin aut Enthalten in Journal of group theory Berlin : de Gruyter, 1998 14(2010), 3 vom: 13. Okt., Seite 341-360 (DE-627)NLEJ248236075 (DE-600)1492030-X 1435-4446 nnns volume:14 year:2010 number:3 day:13 month:10 pages:341-360 extent:20 https://doi.org/10.1515/jgt.2010.052 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 2010 3 13 10 341-360 20 |
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10.1515/jgt.2010.052 doi artikel_Grundlieferung.pp (DE-627)NLEJ247080896 DE-627 ger DE-627 rakwb Alavi, S. Hassan verfasserin aut On triple factorizations of finite groups Walter de Gruyter GmbH & Co. KG 2010 20 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. Walter de Gruyter Online Zeitschriften Praeger, Cheryl E. verfasserin aut Enthalten in Journal of group theory Berlin : de Gruyter, 1998 14(2010), 3 vom: 13. Okt., Seite 341-360 (DE-627)NLEJ248236075 (DE-600)1492030-X 1435-4446 nnns volume:14 year:2010 number:3 day:13 month:10 pages:341-360 extent:20 https://doi.org/10.1515/jgt.2010.052 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 14 2010 3 13 10 341-360 20 |
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Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. |
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Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. |
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Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free. |
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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">NLEJ247080896</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820030046.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2010 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/jgt.2010.052</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">artikel_Grundlieferung.pp</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ247080896</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="100" ind1="1" ind2=" "><subfield code="a">Alavi, S. Hassan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On triple factorizations of finite groups</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">20</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">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Triple factorizations of groups G of the form G = ABA, for proper subgroups A and B, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. This paper introduces and develops a general framework for studying triple factorizations of this form for finite groups, especially nondegenerate ones where G ≠ AB. We identify two necessary and suffcient conditions for subgroups A, B to satisfy G = ABA, in terms of the G-actions on the A-cosets and the B-cosets. This leads to an order (upper) bound for |G| in terms of |A| and |B| which is sharp precisely for the point-line incidence geometries of flag-transitive projective planes. We study in particular the case where G acts imprimitively on the A-cosets, inducing a permutation group that is naturally embedded in a wreath product G0 ≀ G1. This gives rise to triple factorizations for G0, G1 and G0 ≀ G1, respectively. We present a rationale for further study of triple factorizations G = ABA in which A is maximal in G, and both A and B are core-free.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Walter de Gruyter Online Zeitschriften</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Praeger, Cheryl E.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of group theory</subfield><subfield code="d">Berlin : de Gruyter, 1998</subfield><subfield code="g">14(2010), 3 vom: 13. Okt., Seite 341-360</subfield><subfield code="w">(DE-627)NLEJ248236075</subfield><subfield code="w">(DE-600)1492030-X</subfield><subfield code="x">1435-4446</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:14</subfield><subfield code="g">year:2010</subfield><subfield code="g">number:3</subfield><subfield code="g">day:13</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:341-360</subfield><subfield code="g">extent:20</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/jgt.2010.052</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DGR</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">14</subfield><subfield code="j">2010</subfield><subfield code="e">3</subfield><subfield code="b">13</subfield><subfield code="c">10</subfield><subfield code="h">341-360</subfield><subfield code="g">20</subfield></datafield></record></collection>
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