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GL(2,Q)的有限子群
  • 期刊名称：游兴中, 彭大千, 王香芬, GL(2,Q)的有限子群, 吉首大学学报, 30(5):1-3, 20
  • 时间：0
  • 分类：O157.2[理学—数学;理学—基础数学] O152.8[理学—数学;理学—基础数学]
  • 作者机构：[1]中南大学数学科学与计算技术学院,湖南长沙410075, [2]湖南科技学院数学与计算科学系,湖南永州425100
  • 相关基金：国家自然科学基金资助项目（10871205）; 湖南省教育厅科研课题项目（09C444）
  • 相关项目：矩阵几何及有关的代数问题
关键词： 旗传递, 组合设计, 群论, 仿射群, 3-齐次置换群, flag-transitive, combinatorial design, permutation group, affine group, 3-homogeneous permutation groups
中文摘要：

如果一个非平凡的t-设计具有一个旗传递的自同构群,那么t≤6,并且它的自同构群是[（t＋1）/2]齐次本原群.因此,一个旗传递5-（v,k,2）设计的自同构群是3-齐次本原置换群.利用3-齐次本原置换群分类定理,讨论了旗传递5-（v,k,2）设计的分类问题.通过分析5-（v,k,2）设计的组合数量关系和3-齐次本原置换群的性质,部分解决了旗传递5-（v,k,2）设计的分类.证明了如果群G是一个非平凡的5-（v,k,2）设计D的旗传递自同构群,那么Soc（G）=PSL（2,q）,并且q=2^e或3^e.

英文摘要：

If a non-trivial t-design admitting a flag-transitive automorphism group,then t≤6 and its automorphism group is [（t＋1）/2] homogeneous.Therefore,the automorphism group of a flag-transitive 5-（v,k,2） design is a 3-homogeneous permutation group.Using the classification theorem of 3-ho-mogeneous permutation groups,the classification of flag-transitive 5-（v,k,2） designs is discussed.By analyzing the combination quantity relation of 5-（v,k,2） design and the characteristics of 3-homogeneous permutation groups,it is proved that if group G is a flag-transitive automorphism group of a nontri-vial 5-（v,k,2）design,then Soc（G）=PSL（2,q）,and q=2^e or 3^e.

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具有良好传递性的组合结构
期刊论文 56
矩阵几何及有关的代数问题
期刊论文 67 会议论文 19 获奖 4
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