Geodesic
On $\sigma$-permutable subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 61-65.

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Let $\{\sigma_i \mid i\in I\}$ be some partition of the set of all primes $\mathbb{P}$ and let $G$ be a finite group. $G$ is said to be $\sigma$-full if $G$ has a Hall $\sigma_i$-subgroup for all $i$. A subgroup $A$ of $G$ is said to be $\sigma$-permutable in $G$ if $G$ is $\sigma$-full and $A$ permutes with all Hall $\sigma_i$-subgroups $H$ of $G$ (that is, $AH=HA$) for all $i$. In this paper, we give a survey of some recent results on $\sigma$-permutable subgroups of finite groups.
Keywords: finite group, a Robinson $\sigma$-complex of a group, $\sigma$-permutable subgroup, $\sigma$-supersoluble group
Mots-clés : $\sigma$-soluble group, $\sigma$-CS-group. 
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V. M. Selkin; A. N. Skiba. On $\sigma$-permutable subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 3 (2017), pp. 61-65. http://geodesic.mathdoc.fr/item/PFMT_2017_3_a10/

[1] 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

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

[3] L. A. Shemetkov, Formations of finite groups, Nauka, M., 1978 | MR | Zbl

[4] W. Guo, A. N. Skiba, “Finite groups with permutable complete Wielandt sets of subgroups”, J. Group Theory, 18 (2015), 191–200 | DOI | MR | Zbl

[5] A. Ballester-Bolinches, L. M. Ezquerro, Classes of Finite groups, Springer, Dordrecht, 2006 | MR | Zbl

[6] A. N. Skiba, “On $\sigma$-properties of finite groups I”, Probl. Phys. Math. Tech., 2014, no. 4(21), 89–96 | MR | Zbl

[7] A. N. Skiba, On the lattice of the $\sigma$-permutable subgroups of a finite group, arXiv: 1703.01773 [math.GR] | MR

[8] A. Ballester-Bolinches, R. Esteban-Romero, M. Asaad, Products of Finite Groups, Walter de Gruyter, Berlin–New York, 2010 | MR | Zbl

[9] O. H. Kegel, “Sylow-Gruppen und Subnormalteiler endlicher Gruppen”, Math. Z., 78 (1962), 205–221 | DOI | MR | Zbl

[10] W. E. Deskins, “On quasinormal subgroups of finite groups”, Math. Z., 82 (1963), 125–132 | DOI | MR | Zbl

[11] B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin–Heidelberg–New York, 1967 | MR | Zbl

[12] R. K. Agrawal, “Finite groups whose subnormal subgroups permute with all Sylow subgroups”, Proc. Amer. Math. Soc., 47 (1975), 77–83 | DOI | MR | Zbl

[13] D. J. S. Robinson, “The structure of finite groups in which permutability is a transitive relation”, J. Austral. Math. Soc., 70 (2001), 143–159 | DOI | MR | Zbl

[14] R. A. Brice, J. Cossey, “The Wielandt subgroup of a finite soluble groups”, J. London Math. Soc., 40 (1989), 244–256 | DOI | MR

[15] X. Yi, A. N. Skiba, “Some new characterizations of PST-groups”, J. Algebra, 399 (2014), 39–54 | DOI | MR | Zbl

[16] A. N. Skiba, Characterizations of some classes of finite $\sigma$-soluble $P\sigma T$-groups, arXiv: 1704.02509 [math.GR]

[17] A. N. Skiba, A Robinson characterization of finite $P\sigma T$-groups, Preprint, 2017

[18] V. A. Vedernikov, “On some classes of finite groups”, Dokl. Akad. Nauk Belarusi, 32:10 (1988), 872–875 | MR | Zbl

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

[20] P. Schmid, “Subgroups permutable with all Sylow subgroups”, J. Algebra, 207 (1998), 285–293 | DOI | MR | Zbl

[21] G. Pazderski, “On groups for which the lattice of normal subgroups is distributive”, Beiträge Algebra Geom., 24 (1987), 185–200 | MR | Zbl

[22] A. N. Skiba, “On finite groups for which the lattice of $S$-permutable subgroups is distributive”, Arch. Math., 109 (2017), 9–17 | DOI | MR | Zbl

[23] R. Schmidt, Subgroup lattices of groups, Walter de Gruyter, Berlin–New York, 1994 | MR | Zbl