The Representations Between a Group As a Permutation Group and as a Linear Group

Guo Dachang

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The Representations Between a Group As a Permutation Group and as a Linear Group

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- The Representations Between a Group As a Permutation Group and as a Linear Group
- Vol. 14, Issue 4, Pages: 90-93(1997)
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- Online First：16 October 1997，
  
  Published：1997
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郭大昌. 群的置换表示与群的图表示[J]. 广东工业大学学报, 1997, 14(4): 90-93.

Guo Dachang. The Representations Between a Group As a Permutation Group and as a Linear Group[J]. 1997, 14(4): 90-93.
郭大昌. 群的置换表示与群的图表示[J]. 广东工业大学学报, 1997, 14(4): 90-93. DOI：

Guo Dachang. The Representations Between a Group As a Permutation Group and as a Linear Group[J]. 1997, 14(4): 90-93. DOI：

摘要

考虑群Ｇ在一个集合Ω上传递转换作用和把Ω做成Ｇ的Ｃ[Ω]模空间，得到Ｇ作为线性群在Ｃ[Ω]作用，那么二者有怎样的内在联系呢？本文主要结果是：群Ｇ在一个基数为ｐ的集合Ω上的作用是传递的，那么这个置换特征标π有如下分解式：⑴若Ｇ在Ω上的作用是二传递的，则π＝１Ｇ＋χｉ，ｄｅｇχ＝ｐ－１；⑵若Ｇ在Ω上的作用是单本原的，则π＝１Ｇ＋∑ｒｉ＝１χｉ，ｄｅｇχｉ＝ｍ，ｉ＝１，２，…，ｒ，ｐ－１＝ｍ·ｒ．此处数ｒ称为Ｇ的秩．

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郭大昌. 交错群A5的4度连通对称图的分类[J]. 广东机械学院学报. 1997(01)

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