Normalizers of nilpotent residuals

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• 作者：Lü Gong ; I. M. Isaacs
• 关键词：Subnormal ; Nilpotent ; Residual
• 刊名：Archiv der Mathematik
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：108
• 期：1
• 页码：1-7
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-8938
• 卷排序：108

文摘

Let M be a subgroup of a finite group G, and suppose that M normalizes the nilpotent residual \(H^\infty \) of every non-subnormal subgroup H of G. We show that M must also normalize the nilpotent residuals of the subnormal subgroups of G. We also prove a similar result for the solvable residual.