Geodesic
A criterion for the $\sigma$-subnormality of a subgroup in a finite $3'$-group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 36-43

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For a partition $\sigma$ of the set $\mathbb{P}$ of all primes, it is solved, that if a subgroup $H$ of a finite $3'$-group $G$ is $\sigma$-subnormal in $$ for any $x \in G$, then $H$ is $\sigma$-subnormal in $G$.
Keywords: finite group, $\sigma$-subnormal subgroup, subnormal subgroup, Suzuki group. 
@article{IVM_2020_8_a3,
     author = {S. F. Kamornikov and V. N. Tyutyanov},
     title = {A criterion for the $\sigma$-subnormality of a subgroup in a finite $3'$-group},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {36--43},
     publisher = {mathdoc},
     number = {8},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_8_a3/}
}
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S. F. Kamornikov; V. N. Tyutyanov. A criterion for the $\sigma$-subnormality of a subgroup in a finite $3'$-group. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 36-43. http://geodesic.mathdoc.fr/item/IVM_2020_8_a3/