Finite groups with a self-centralizing subgroup of order 4
Finite groups with a self-centralizing subgroup of order 4
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DOI：
10.1017/s1446788700004511
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发表时间：
1967-11
影响因子：
0.7
通讯作者：
W. J. Wong
中科院分区：
文献类型：
--
作者：
W. J. Wong
Suzuki [9]、Gorenstein和Walter [6]以及本文作者[11]研究了具有4阶子群的有限群类。本文的主要目的是利用Zassenhaus [12]的一个早期结果加强[11]的定理5。特别是，我们发现所有的群体的类是核心免费的，即没有非平凡的正规子群的奇数阶。作为应用，我们给出了一类本原置换群的判定。
The class of finite groups having a subgroup of order 4 which is its own centralizer has been studied by Suzuki [9], Gorenstein and Walter [6], and the present author [11]. The main purpose of this paper is to strengthen Theorem 5 of [11] by using an early result of Zassenhaus [12]. In particular, we find all groups of the class which are core-free, i.e. which have no nontrivial normal subgroup of odd order. As an application, we make a determination of a certain class of primitive permutation groups.