Geodesic
On $\sigma_3$-nilpotent finite groups
Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 52-55.

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Throughout the article all groups are finite and $G$ always denotes finite group; $\mathbb{P}$ is the set of all prime numbers and $\mathfrak{J}$ is some class of groups, closed under extensions, homomorphic images and subgroups. In this paper, $\sigma_3=\{\sigma_0\}\cup\{\sigma_i\mid i\in I\}$ is a partition of the set $\mathbb{P}$, i. e. $\mathbb{P}=\sigma_0\cup\bigcup_{i\in I}\sigma_i$ and $\sigma_i\cap\sigma_j=\varnothing$ for all indices $i\ne j$ from $\{0\}\cup I$, for which $\mathfrak{J}$ is a class of $\sigma_0$-groups with $\pi(\mathfrak{J})=\sigma_0$. The group $G$ is called: $\sigma_3$-primary if $G$ is either an $\mathfrak{J}$-group or a $\sigma_i$-group for some $i\ne0$; $\sigma_3$-nilpotent if $G$ is the direct product of some $\sigma_3$-primary groups. Finite $\sigma_3$-nilpotent groups are characterized.
Keywords: finite group, $\sigma_3$-subnormal subgroup, $\sigma_3$-nilpotent group, Hall subgroup.
Mots-clés : $\sigma_3$-soluble group 
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I. M. Dergacheva; I. P. Shabalina; E. A. Zadorozhnyuk; I. A. Sobol'. On $\sigma_3$-nilpotent finite groups. Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 52-55. http://geodesic.mathdoc.fr/item/PFMT_2023_2_a9/

[1] A.N. Skiba, “O $\sigma$-svoistvakh konechnykh grupp I”, Problemy fiziki, matematiki i tekhniki, 2014, no. 4 (21), 89–96

[2] A.N. Skiba, “O $\sigma$-svoistvakh konechnykh grupp II”, Voprosy fiziki, matematiki i tekhniki, 3:24 (2015), 67–81

[3] A.N. Skiba, “O $\sigma$-svoistvakh konechnykh grupp III”, Problemy fiziki, matematiki i tekhniki, 2016, no. 1 (26), 52–62

[4] A.N. Skiba, “On some results in the theory of finite partially soluble groups”, Commun. Math. Stat., 4:3 (2016), 281–309 | DOI | MR | Zbl

[5] A.N. Skiba, “On $\sigma$-subnormal and $\sigma$-permutable subgroups of finite groups”, J. Algebra, 436 (2015), 1–16 | DOI | MR | Zbl

[6] A.N. Skiba, “Some characterizations of finite $\sigma$-soluble $P\sigma T$-groups”, J. Algebra, 495:1 (2018), 114–129 | DOI | MR | Zbl

[7] A.N. Skiba, “On sublattices of the subgroup lattice defined by formation Fitting sets”, J. Algebra, 550 (2020), 69–85 | DOI | MR | Zbl

[8] A-Ming Liu, W. Guo, I.N. Safonova, A.N. Skiba, “G-covering subgroup systems for some classes of $\sigma$-soluble groups”, J. Algebra, 585 (2021), 280–293 | DOI | MR

[9] Xin-Fang Zhang, W. Guo, I.N. Safonova, A.N. Skiba, “A Robinson description of finite $P\sigma T$-groups”, J. Algebra, 2023 | DOI | MR

[10] K. Doerk, T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin–New York, 1992 | MR

[11] A.N. Skiba, “A generalization of a Hall theorem”, J. Algebra and its Application, 15:5 (2016) | DOI | MR