Wielandt subgroups of certain finite groups
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 121-131.

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The Wielandt subgroup of a finite group $G$ is defined as $w(G)={\bigcap\limits_{H \mathbin{{\lhd} {\lhd}} G}N_{G}(H)}$. In this paper, this subgroup is computed for certain finite groups.
Keywords: finite group, Wielandt subgroup, subnormal subgroup.
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H. B. Shelash; A. R. Ashrafi. Wielandt subgroups of certain finite groups. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 121-131. http://geodesic.mathdoc.fr/item/INTO_2020_177_a13/

[1] Abbaspour M. H., Behravesh H., “Quasi-permutation representations of $2-$groups satisfying the Hasse principle”, Ric. Math., 59 (2010), 49–57 | DOI | MR | Zbl

[2] Ballester-Bolinches A., Esteban-Romero R., “On finite $T-$groups”, J. Austr. Math. Soc., 75:2 (2003), 181–191 | DOI | MR | Zbl

[3] Bianchi M., Gillio Berta Mauri A., Herzog M., Verardi L., “On finite solvable groups in which normality is a transitive relation”, J. Group Theory., 3:2 (2000), 147–156 | DOI | MR | Zbl

[4] Cavior S. R., “The subgroups of the dihedral groups”, Math. Mag., 48 (1975), 107 | DOI | MR | Zbl

[5] Chin A., Newell P., “A charecterization of higher order Wielandt subgroups and some application”, Missouri J. Math. Sci., 21:3 (2009), 206–209 | DOI | MR | Zbl

[6] Darafsheh M. R., Poursalavati N. S., “On the existence of the orthogonal basis of the symmetry classes of tensors associated with certain groups”, SUT J. Math., 37:1 (2001), 1–17 | MR | Zbl

[7] James G., Liebeck M., Representations and characters of groups, Cambridge Univ. Press, New York, 2001 | MR | Zbl

[8] Kurzweil H., Stellmacher B., The theory of finite groups: An introduction, Springer-Verlag, New York, 2004 | MR | Zbl

[9] Müller K. H., “Schwachnormale Untergruppen: Eine gemeinsame Verallgemeinerung der normalen und normalisatorgleichen Untergruppen”, Rend. Sem. Mat. Univ. Padova, 36 (1966), 129–157 | MR | Zbl

[10] Robinson D. J. S., “A note on finite groups in which normality is transitive”, Proc. Am. Math. Soc., 19 (1968), 933–937 | DOI | MR | Zbl

[11] Shelash H. B., Ashrafi A. R., “Computing maximal and minimal subgroups with respect to a given property in certain finite groups”, Quasigroups Rel. Syst., 27:1 (2019), 133–146 | MR | Zbl

[12] Tărnăuceanu M., Contributions to the study of subgroup lattices, Matrix Rom, Bucharest, 2016 | MR

[13] “The GAP Team”, GAP – Groups, Algorithms, and Programming, 2014, Version 4.7.5

[14] Wielandt H., “Eine Verallgemeinerung der invarianten Untergruppen”, Math. Z., 45 (1939), 209–244 | DOI | MR

[15] Wielandt H., “Über den Normalisator der Subnormalen Untergruppen”, Math. Z., 69 (1958), 463–465 | DOI | MR | Zbl