| Strongly Regular $(\alpha,\beta)$-Families and Translation Strongly Regular $(\alpha,\beta)$-Geometries |
| Received:June 22, 2006 Revised:April 18, 2008 |
| Key Words:
projective space strongly regular $(\alpha,\beta)$-regulus strongly regular $(\alpha,\beta)$-geometry.
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| Fund Project:the Scientific Research Start-Up Foundation of Qingdao University of Science and Technology in China. (No.0022327). |
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| Abstract: |
| In this paper, we introduce the concept of a strongly regular $(\alpha,\beta)$-family. It generalizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular $(\alpha,\beta)$-geometries from strongly regular $(\alpha,\beta)$-families. Furthermore, we prove that each strongly regular $(\alpha,\beta)$-geometry constructed from a strongly regular $(\alpha,\beta)$-regulus translation is isomorphic to a translation strongly regular $(\alpha,\beta)$-geometry; while $t-r>\beta$, the converse is also true. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.024 |
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