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：

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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。