Geodesic
A criterion of unrecognizability by spectrum for finite groups
Algebra i logika, Tome 51 (2012) no. 2, pp. 239-243.

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It is proved that a finite group $G$ is unrecognizable by spectrum if and only if there exists a group isospectral to $G$ containing a nontrivial soluble normal subgroup.
Keywords: finite group, soluble normal subgroup, spectrum. 
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V. D. Mazurov; W. J. Shi. A criterion of unrecognizability by spectrum for finite groups. Algebra i logika, Tome 51 (2012) no. 2, pp. 239-243. http://geodesic.mathdoc.fr/item/AL_2012_51_2_a5/

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