Geodesic
On the Kegel--Wielandt $\sigma$-Problem
Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 564-570

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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 in a finite group is given. It is proved that, if a complete Hall set of type $\sigma$ is reduced into a subgroup $H$ of a $\sigma$-complete finite group $G$ all of whose non-Abelian composition factors are alternating groups, Suzuki groups, or Ree groups, then $H$ is $\sigma$-subnormal in $G$.
Keywords: finite group, $\sigma$-subnormal subgroup, Hall subgroup, complete Hall set, Ree group. 
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     author = {S. F. Kamornikov and V. N. Tyutyanov},
     title = {On the {Kegel--Wielandt} $\sigma${-Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {564--570},
     publisher = {mathdoc},
     volume = {109},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a6/}
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S. F. Kamornikov; V. N. Tyutyanov. On the Kegel--Wielandt $\sigma$-Problem. Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 564-570. http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a6/