Geodesic
On the center of a graph defined by Schmidt subgroups of a finite group
Problemy fiziki, matematiki i tehniki, no. 4 (2022), pp. 73-79.

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A Schmidt group is a non-nilpotent group whose proper subgroups are nilpotent. Schmidt graph of a finite group $G$ is the prime graph with the vertex set $\pi(G)$ in which $(p,q)$ is an edge if and only if $G$ has a Schmidt subgroup whose order is divisible by $pq$. In the paper the relationship of Schmidt graph properties with group properties is studied.
Keywords: finite group, prime graph, Schmidt group, Schmidt graph
Mots-clés : soluble graph, centre of graph. 
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P. V. Bychkov; S. F. Kamornikov; V. N. Tyutyanov. On the center of a graph defined by Schmidt subgroups of a finite group. Problemy fiziki, matematiki i tehniki, no. 4 (2022), pp. 73-79. http://geodesic.mathdoc.fr/item/PFMT_2022_4_a11/

[1] J.S. Williams, “Prime graph components of finite groups”, J. Algebra, 69:2 (1981), 487–513 | DOI | MR | Zbl

[2] V.D. Mazurov, “Raspoznavanie konechnykh grupp po mnozhestvu poryadkov ikh elementov”, Algebra i logika, 37:6 (1998), 651–666 | Zbl

[3] S. Abe, N. Iiyori, “A generalization of prime graphs of finite groups”, Hokkaido Math. J., 29:2 (2000), 391–407 | DOI | MR | Zbl

[4] B. Amberg, A. Carocca, L.S. Kazarin, “Criteria for the solubility and non-simplicity of finite groups”, J. Algebra, 285 (2005), 58–72 | DOI | MR | Zbl

[5] L.S. Kazarin, A. MartinezPastor, M.D. Perez-Ramos, “On the Sylow graph of a group and Sylow normalizers”, Isr. J. Math., 186 (2011), 251–271 | DOI | MR | Zbl

[6] V.N. Knyagina, V.S. Monakhov, “O konechnykh gruppakh s nekotorymi subnormalnymi podgruppami Shmidta”, Sib. mat. zhurn., 45:6 (2004), 1316–1322 | Zbl

[7] A.F. Vasilev, V.I. Murashko, “Arifmeticheskie grafy i klassy konechnykh grupp”, Sib. mat. zhurn., 60:1 (2019), 66–84 | Zbl

[8] V.I. Murashko, “Gruppy s zadannymi sistemami podgrupp Shmidta”, Sib. mat. zhurn., 60:2 (2019), 429–440

[9] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin - New York, 1992, 891 pp. | MR

[10] O.Yu. Shmidt, “Gruppy, vse podgruppy kotorykh spetsialnye”, Mat. sb., 31:3–4 (1924), 366–372

[11] Yu.A. Golfand, “O gruppakh, vse podgruppy kotorykh spetsialnye”, DAN SSSR, 60:8 (1948), 1313–1315 | Zbl

[12] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp.

[13] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985, 352 pp. | MR

[14] L.S. Kazarin, V.N. Tyutyanov, “On centers of soluble graphs”, Sib. elektron. matem. izv., 18:2 (2021), 1517–1530 | MR | Zbl

[15] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985, 252 pp. | MR | Zbl