Finite Linear Groups of Degree Seven. I
Finite Linear Groups of Degree Seven. I
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DOI：
10.4153/cjm-1969-115-9
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
D. B. Wales
中科院分区：
文献类型：
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作者：
D. B. Wales
1. 1.本文是第二次在一系列文件讨论线性群的素数程度，第一次是（8）。本文只讨论7次线性群。因此，G是一个有限群，它有一个7度的忠实不可约复表示X，X是么模的本原的。X的特征是x-除了这里p= 7之外，使用（8）的符号。在§§ 2和3中给出了关于3-Sylow群和5-Sylow群的一些一般定理。§ 4给出了当G具有非交换的7-Sylow群时的结果。这与案件相对应|P| =73或|P| = 74。证据在§§ 5和6中给出。在随后的文件中的结果时，Pis阿贝尔将被给予。
1. 1. This paper is the second in a series of papers discussing linear groups of prime degree, the first being (8). In this paper we discuss only linear groups of degree 7. Thus, G is a finite group with a faithful irreducible complex representation Xof degree 7 which is unimodular and primitive. The character of Xis x- The notation of (8) is used except here p= 7. Thus Pis a 7-Sylow group of G.In §§ 2 and 3 some general theorems about the 3-Sylow group and 5-Sylow group are given. In § 4 the statement of the results when Ghas a non-abelian 7-Sylow group is given. This corresponds to the case |P| =73 or |P|= 74. The proof is given in §§ 5 and 6. In a subsequent paper the results when Pis abelian will be given.