Journal of Group Theory | 2019
On the nilpotency of the solvable radical of a finite group isospectral to a simple group
Abstract
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.