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On the nilpotency of the solvable radical of a finite group isospectral to a simple group
Journal of Group Theory ( IF 0.4 ) Pub Date : 2020-05-01 , DOI: 10.1515/jgth-2019-0109 Nanying Yang 1 , Mariya A. Grechkoseeva 2 , Andrey V. Vasil’ev 2
Journal of Group Theory ( IF 0.4 ) Pub Date : 2020-05-01 , DOI: 10.1515/jgth-2019-0109 Nanying Yang 1 , Mariya A. Grechkoseeva 2 , Andrey V. Vasil’ev 2
Affiliation
Abstract We refer to the set of the orders of elements of a finite group as its spectrum and say that groups are isospectral if their spectra coincide. We prove that, except for one specific case, the solvable radical of a nonsolvable finite group isospectral to a finite simple group is nilpotent.
中文翻译:
关于单群等谱的有限群的可解根的幂零性
摘要 我们将有限群的元素阶数集合称为它的谱,如果它们的谱重合,则称这些群是等谱的。我们证明,除了一种特殊情况外,等谱于有限单群的不可解有限群的可解根是幂零的。
更新日期:2020-05-01
中文翻译:
关于单群等谱的有限群的可解根的幂零性
摘要 我们将有限群的元素阶数集合称为它的谱,如果它们的谱重合,则称这些群是等谱的。我们证明,除了一种特殊情况外,等谱于有限单群的不可解有限群的可解根是幂零的。