Geodesic
Non-radicality of the class $E_\pi$-groups
Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 35-39

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In the note it is proven that the class $E_\pi$ of all finite groups possessing $\pi$-Hall subgroups, for given set of primes $\pi,$ is not radical (i.e., the product of normal $E_\pi$-subgroups of a finite group is not necessary an $E_\pi$-group). 
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E. P. Vdovin; D. O. Revin. Non-radicality of the class $E_\pi$-groups. Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 35-39. http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a3/