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首页> 外文期刊>Journal of group theory >Fischer subgroups, Fitting height, and pronormality
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Fischer subgroups, Fitting height, and pronormality

机译：菲舍尔（Fischer）子组，拟合高度和前态

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Several authors have studied the relationship between Fischer F-subgroups and F-injectors of a finite soluble group. Fischer [6] proved that when F is a special kind of Fitting set, now called a Fischer set of G, the Fischer F-subgroups and the F-injectors of G coincide. A bit more generally, Anderson [1] came to the same conclusion when the Fischer F-subgroups of H are normally embedded in H for each subgroup H of G. In [4] and [5] respectively, the second author proved the same thing when the Fischer F-subgroups of G are either subnormally embedded or locally pronormal in G, and when they are system permutable. The first author [2] provided the original example of a Fischer F-subgroup that is not an F-injector, where F is a Fitting class; later Doerk and Hawkes [3, VIII(4.9)] gave an example of a group G and a Fitting set F such that the Fischer F-subgroups of G are not injectors for F or for any other Fitting set of G.
机译：几位作者研究了Fischer F子群与有限可溶基团的F注入子之间的关系。 Fischer [6]证明，当F是一种特殊的Fitting集时，现在称为G的Fischer集，Fischer F子群和G的F注入子是重合的。更一般地说，当G的每个子组H的Fischer F子组通常嵌入H中时，Anderson [1]得出相同的结论。第二作者分别在[4]和[5]中证明了相同的结论。当G的Fischer F子群在G中是次正规嵌入的或局部原正态时，并且它们是系统可置换的。第一作者[2]提供了不是F注入器的Fischer F子组的原始示例，其中F是Fitting类。后来Doerk和Hawkes [3，VIII（4.9）]给出了G组和拟合集F的示例，这样G的Fischer F子组不是F或任何其他G拟合集的注射器。

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