Geodesic
On the Kegel–Wielandt $\sigma$-Problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 121-129 Cet article a éte moissonné depuis la source Math-Net.Ru

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For an arbitrary partition $\sigma$ of the set $\mathbb{P}$ of all primes, a sufficient condition for the $\sigma$-subnormality of a subgroup of a finite group is given. It is proved that the Kegel–Wielandt $\sigma$-problem has a positive solution in the class of all finite groups all of whose nonabelian composition factors are alternating groups, sporadic groups, or Lie groups of rank $1$.
Keywords: finite group, $\sigma$-subnormal subgroup, Kegel–Wielandt $\sigma$-problem, Hall subgroup, complete Hall set. 
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S. F. Kamornikov; V. N. Tyutyanov. On the Kegel–Wielandt $\sigma$-Problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 121-129. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a9/

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