Half-Transitive Automorphism Groups
Half-Transitive Automorphism Groups
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DOI：
10.4153/cjm-1966-122-5
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发表时间：
1966
期刊：
影响因子：
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通讯作者：
I. Isaacs;D. Passman
中科院分区：
文献类型：
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作者：
I. Isaacs;D. Passman
设G是有限群，A是G的自同构群.显然，A充当G#上的置换群，G #是G的非单位元素的集合。我们假设这个置换表示是半传递的，也就是说所有的轨道都有相同的大小。当A自由作用于G上时，会出现这种特殊情况。本文研究了剩余或非不动点自由的情形。我们首先证明了对于某个素数q，G必是初等交换g-群，且A作用在G上不可约。然后我们对所有这样的出现进行分类，其中A是p-群。
Let G be a finite group and A a group of automorphisms of G. Clearly A acts as a permutation group on G#, the set of non-identity elements of G. We assume that this permutation representation is half transitive, that is all the orbits have the same size. A special case of this occurs when A acts fixed point free on G. In this paper we study the remaining or non-fixed point free cases. We show first that G must be an elementary abelian g-group for some prime q and that A acts irreducibly on G. Then we classify all such occurrences in which A is a p-group.