Simple non abelian group with $D_\pi$ Schmidt subgroups
Problemy fiziki, matematiki i tehniki, no. 2 (2012), pp. 95-98.

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Let $G$ be a finite simple group, $S$ be its Hall Schmidt $\pi$-subgroup. If $2\in\pi$ then $G$ is not a $D_\pi$-group. If $2\notin\pi$ and $G\notin\{A_n(q),^2 A_n(q)\}$ then $G$ is a $D_\pi$-group.
Mots-clés : group, simple group, $D_\pi$-group.
Keywords: subgroup, Hall Schmidt $\pi$-subgroup
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V. N. Tyutyanov; P. V. Bychkov. Simple non abelian group with $D_\pi$ Schmidt subgroups. Problemy fiziki, matematiki i tehniki, no. 2 (2012), pp. 95-98. http://geodesic.mathdoc.fr/item/PFMT_2012_2_a15/

[1] D. Gorenstein, Finite groups, Harper and Row, New-York, 1968 | MR | Zbl

[2] J. H. Conway et al., Atlas of Finite Groups, Oxford, 1985

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

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

[5] V. D. Mazurov, S. A. Syskin, “O konechnykh gruppakh so spetsialnymi silovskimi 2-podgruppami”, Matem. zam., 14:2 (1973), 217–222 | MR

[6] R. Hartley, “Determination of the ternary collineation groups whose coefficients lie in the $GF(2^n)$”, Ann. of Math., 27 (1925), 140–158 | DOI | MR | Zbl

[7] D. O. Revin, Khollovy podgruppy konechnykh grupp, Dis. ... d-ra fiz.-matem. nauk: 01.01.06, Novosibirsk, 2008, 232 pp.

[8] H. Wielandt, “Zum Satz von Sylow”, Math. Z., 60 (1954), 407–409 | DOI | MR

[9] P. Hall, “Theorems like Sylow's”, Proc. London Math. Soc., 3:6 (1956), 286–304 | DOI | MR | Zbl

[10] B. Huppert, Endliche Gruppen, v. I, Springer-Verlag, Berlin–Heidelberg–New York, 1967, 793 pp. | MR | Zbl

[11] P. Kleidman, “The maximal subgroups of Chevalley groups $G_2(q)$ with $q$ odd, the Ree groups $^2G_2(q)$, and their automorphism groups”, J. Algebra, 117 (1988), 30–71 | DOI | MR | Zbl

[12] E. P. Vdovin, D. O. Revin, “Khollovy podgruppy nechetnogo poryadka v konechnykh gruppakh”, Algebra i logika, 41:1 (2002), 15–56 | MR | Zbl