Geodesic
On finite non-simple $4$-primary groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 695-708.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a finite $4$-primary group with disconnected prime graph, $\pi_1(G) = \{2,3,r\}$ for $r \in \{5,7\}$, $G/F(G)$ is a nonsimple almost simple group non isomorphic to $S_4(9).2$. In this paper, all chief factors of $G$ are described.
Keywords: finite group, prime graph, $4$-primary group, chief factor. 
@article{SEMR_2014_11_a20,
     author = {I. V. Khramtsov},
     title = {On finite non-simple $4$-primary groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {695--708},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a20/}
}
TY  - JOUR
AU  - I. V. Khramtsov
TI  - On finite non-simple $4$-primary groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2014
SP  - 695
EP  - 708
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2014_11_a20/
LA  - ru
ID  - SEMR_2014_11_a20
ER  - 
%0 Journal Article
%A I. V. Khramtsov
%T On finite non-simple $4$-primary groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2014
%P 695-708
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2014_11_a20/
%G ru
%F SEMR_2014_11_a20
I. V. Khramtsov. On finite non-simple $4$-primary groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 695-708. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a20/

[1] S. Astill, K. Parker, R. Valdeker, “O gruppakh, v kotorykh tsentralizatory elementov poryadka $5$ yavlyayutsya $5$-gruppami”, Sib. mat. zhurn., 53:3 (2012), 967–977 | MR | Zbl

[2] S. Dolfi, E. Dzhabara, M. S. Lyuchido, “$C55$-gruppy”, Sib. mat. zhurn., 45:6 (2004), 1285–1298 | MR | Zbl

[3] A. S. Kondratev, I. V. Khramtsov, “O konechnykh triprimarnykh gruppakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 3, 2010, 150–158

[4] A. S. Kondratev, I. V. Khramtsov, “O konechnykh chetyreprimarnykh gruppakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 4, 2011, 142–159

[5] A. S. Kondratev, I. V. Khramtsov, “O konechnykh neprostykh triprimarnykh gruppakh”, Sib. elektron. matem. izv., 9 (2012), 472–477 | MR

[6] A. S. Kondratev, I. V. Khramtsov, “O konechnykh gruppakh, kotorye imeyut nesvyaznyi graf prostykh chisel i kompozitsionnyi faktor, izomorfnyi gruppe $L_3(17)$”, Materialy konf. "Algebra i matematicheskaya logika: teoriya i prilozheniya", Izd-vo Kazan. un-ta, Kazan, 2014, 81–82

[7] Ch. Kertis, I. Rainer, Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969, 668 pp. | MR

[8] C. Jansen, K. Lux, R. Parker, R. Wilson, An atlas of Brauer characters, Clarendon Press, Oxford, 1995 | MR | Zbl

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

[10] R. Burkhardt, “Die Zerlegungsmatrizen der Gruppen $PSL(2,p^f)$-groups”, J. Algebra, 40:1 (1976), 75–96 | DOI | MR | Zbl

[11] B. Huppert, N. Blackburn, Finite groups, v. II, Springer-Verlag, Berlin, 1982 | MR

[12] W. Nickel, Endliche Körper in dem gruppentheoretischen Programmsystem GAP, Diploma thesis, RWTH, Aachen, 1988

[13] The GAP Group, GAP — Groups, Algorithms, and Programming, Ver. 4.7.4, , 2014 http://www.gap-system.org

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