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强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何
引用本文:李秀丽.强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何[J].数学研究与评论,2008,28(4):928-934.
作者姓名:李秀丽
作者单位:青岛科技大学数理学院, 山东 青岛 266042
基金项目:青岛科技大学科研启动基金(No.0022327).
摘    要:本文给出了强正则$(\alpha,\beta)-$族的概念,它是4]和5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(\alpha,\beta)-$族构造强正则$(\alpha,\beta)-$几何的方法.另外,本文还证明了由强正则$(\alpha,\beta)-$线汇构造的强正则$(\alpha,\beta)-$几何是平移强正则$(\alpha,\beta)-$几何;当$t-r>\beta$时,反之亦成立.

关 键 词:射影空间  强正则$(\alpha  \beta)-$线汇  强正则$(\alpha  \beta)-$族  强正则  $(\alpha  \beta)-$几何.
收稿时间:2006/6/22 0:00:00
修稿时间:2008/4/18 0:00:00

Strongly Regular $(\alpha,\beta)$-Families and Translation Strongly Regular $(\alpha,\beta)$-Geometries
LI Xiu Li.Strongly Regular $(\alpha,\beta)$-Families and Translation Strongly Regular $(\alpha,\beta)$-Geometries[J].Journal of Mathematical Research and Exposition,2008,28(4):928-934.
Authors:LI Xiu Li
Institution:School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong 266042, China
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.
Keywords:projective space  strongly regular $(\alpha  \beta)$-regulus  strongly regular $(\alpha  \beta)$-geometry  
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