| 郭文彬.关于多克托罗夫定理[J].数学研究及应用,1996,16(1):108~110 |
| 关于多克托罗夫定理 |
| On Doctorov′s Theorem |
| 投稿时间：1993-04-04 |
| DOI：10.3770/j.issn:1000-341X.1996.01.021 |
| 中文关键词: 群论 抽象群 超可解群． |
| 英文关键词:group abstact group supersolvable group. |
| 基金项目: |
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| 摘要点击次数: 1980 |
| 全文下载次数: 1164 |
| 中文摘要: |
| 本文将多克托罗夫定理的条件减弱，得到了这样的定理：设Ｇ是有限群．如果Ｇ的每个西洛子群的正规化子有Ｈａｉｌ补，则Ｇ为σ－西洛塔解；此外，如果这些补的Ｆｉｔｔｉｎｇ子群是循环群，则Ｇ为超可解群． |
| 英文摘要: |
| In this paper the conditions of Doctorov' theorem are weakened, and the following theorem is proved. Let G be a finite group. If the normalizer of each Sylow subgroup of G has Hall complement, then G is a dispersive group. Moreover, if the Fitting subgroups of these complements are cyclic, then G is supersolvable. |
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