Geodesic
Nilpotency of the derived subgroup of a finite group with semisubnormal Schmidt subgroups
Problemy fiziki, matematiki i tehniki, no. 3 (2022), pp. 86-89.

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A non-nilpotent finite group all of whose proper subgroups are nilpotent is called a Schmidt group. A subgroup $A$ is called seminormal in a group $G$ if there exists a subgroup $B$ such that $G=AB$ and $AB_1$ is a proper subgroup of $G$ for each proper subgroup $B_1$ of $B$. If $A$ is either subnormal in $G$ or seminormal in $G$, then the subgroup $A$ is called semisubnormal in $G$. We establish the nilpotency of the derived subgroup of a group all of whose Schmidt subgroups are semisubnormal.
Keywords: finite group, Schmidt subgroup, seminormal subgroup, subnormal subgroup. 
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V. N. Kniahina. Nilpotency of the derived subgroup of a finite group with semisubnormal Schmidt subgroups. Problemy fiziki, matematiki i tehniki, no. 3 (2022), pp. 86-89. http://geodesic.mathdoc.fr/item/PFMT_2022_3_a14/

[1] O.Yu. Shmidt, “Gruppy, vse podgruppy kotorykh spetsialnye”, Matematicheskii sbornik, 31 (1924), 366–372

[2] N.F. Kuzennyi, S.S. Levischenko, “Konechnye gruppy Shmidta i ikh obobscheniya”, Ukrainskii matematicheskii zhurnal, 43:7–8 (1991), 963–968

[3] V.S. Monakhov, “Podgruppy Shmidta, ikh suschestvovanie i nekotorye prilozheniya”, Ukrainskii matematicheskii kongress, sb. tr., In-t matem. NAN Ukrainy, Kiev, 2002, 81–90

[4] V.N. Knyagina, V.S. Monakhov, “O konechnykh gruppakh s nekotorymi cubnormalnymi podgruppami Shmidta”, Sibirskii matematicheskii zhurnal, 45:6 (2004), 1316–1322 | Zbl

[5] V.A. Vedernikov, “Konechnye gruppy s subnormalnymi podgruppami Shmidta”, Algebra i logika, 44:6 (2007), 669–687

[6] Kh.A. Al-Sharo, A.N. Skiba, “On finite groups with $\sigma$-subnormal Schmidt subgroups”, Communications in Algebra, 45 (2017), 4158–4165 | DOI | MR | Zbl

[7] V.N. Knyagina, V.S. Monakhov, “Finite groups with Hall Schmidt subgroups”, Publicationes Mathematicae Debrecen, 81:3–4 (2012), 341–350 | DOI | MR | Zbl

[8] V.V. Podgornaya, “Polunormalnye podgruppy i sverkhrazreshimost konechnykh grupp”, Vestsi NAN Belarusi. Ser. fiz.-matem. navuk, 2000, no. 4, 22–25

[9] V.S. Monakhov, “Konechnye gruppy s polunormalnoi khollovoi podgruppoi”, Matematicheskie zametki, 80:4 (2006), 573–581 | DOI | Zbl

[10] W. Guo, “Finite groups with seminormal Sylow subgroups”, Acta Mathematica Sinica, 24:10 (2008), 1751–1758 | DOI | MR

[11] V.N. Knyagina, V.S. Monakhov, “Konechnye gruppy s polunormalnymi podgruppami Shmidta”, Algebra i logika, 46:4 (2007), 448–458 | Zbl

[12] V.S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006, 207 pp.

[13] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 271 pp.

[14] J.H. Conway et al., Atlas of finite groups: Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford, 1985, 286 pp. | MR | Zbl

[15] V.S. Monakhov, “Ob indeksakh maksimalnykh podgrupp konechnykh razreshimykh grupp”, Algebra i logika, 43:4 (2004), 411–424 | Zbl