Geodesic
On some aspects of the Kegel-Wielandt $\sigma$-problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 18-28

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For a partition $\sigma$ of the set $\mathbb{P}$ of all primes, a sufficient criterion for $\sigma$-subnormality of a subgroup in finite group is given. It is proved, that Kegel-Wielandt $\sigma$-problem has a positive solution in the class of all finite groups, in which all non-abelian composition factors are either alternating groups, or Suzuki groups, or sporadic groups.
Keywords: finite group, Hall subgroup, $\sigma$-subnormal subgroup, subnormal subgroup
Mots-clés : sporadic group. 
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     author = {S. F. Kamornikov and V. N. Tyutyanov},
     title = {On some aspects of the {Kegel-Wielandt} $\sigma$-problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {18--28},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
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}
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S. F. Kamornikov; V. N. Tyutyanov. On some aspects of the Kegel-Wielandt $\sigma$-problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 18-28. http://geodesic.mathdoc.fr/item/IVM_2022_2_a1/