On products of $\pi$-solvable finite groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 109-120 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, we study finite groups having a triple factorization $G=AB=AC=BC$, where the factors $A$, $B$, and $C$ are $\pi$-solvable subgroups of the group $G$ for some set $\pi$ of primes. This problem seems to have been first formulated by A. F. Vasil'ev and A. K. Furs in 2021 at the conference dedicated to the 90th anniversary of the birth of A. I. Starostin.
Keywords: finite group, subgroup, character, representation, factorization.
@article{TIMM_2023_29_4_a8,
     author = {L. S. Kazarin},
     title = {On products of $\pi$-solvable finite groups},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {109--120},
     year = {2023},
     volume = {29},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a8/}
}
TY  - JOUR
AU  - L. S. Kazarin
TI  - On products of $\pi$-solvable finite groups
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2023
SP  - 109
EP  - 120
VL  - 29
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a8/
LA  - ru
ID  - TIMM_2023_29_4_a8
ER  - 
%0 Journal Article
%A L. S. Kazarin
%T On products of $\pi$-solvable finite groups
%J Trudy Instituta matematiki i mehaniki
%D 2023
%P 109-120
%V 29
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a8/
%G ru
%F TIMM_2023_29_4_a8
L. S. Kazarin. On products of $\pi$-solvable finite groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 109-120. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a8/

[1] Wielandt H., “Uber die Normalstructur von mehrfach factorizierten Gruppen”, J. Austral. Math. Soc., 1 (1960), 143–146 | DOI | MR | Zbl

[2] Kazarin L.S., “Factorizations of finite groups by solvable subgroups”, Ukrainian Math. J., 43 (1992), 883–886 | DOI | MR

[3] Pennington E., “Trifactorisable groups”, Bull. Austral. Math. Soc., 8 (1973), 461–469 | DOI | MR | Zbl

[4] Kazarin L.S., Martinez-Pastor A., Perez-Ramos M.D., “Finite trifactorized groups and $\pi$-decomposable groups”, Bull. Austral. Math. Soc., 97:2 (2018), 218–228 | DOI | MR | Zbl

[5] Gorenstein D., Finite groups, Harper and Row, NY, 1968, 642 pp. | MR | Zbl

[6] Herzog M., “On finite simple groups of order divisible by three primes only”, J. Algebra, 10:3 (1968), 383–388 | DOI | MR | Zbl

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

[8] Kazarin L.S., Tutanov V.N., “On centers of soluble graph”, Sib. elektron. mat. izv., 18:2 (2021), 1517–1530 | DOI | MR | Zbl

[9] Liebeck M.W., Praeger C.E., Saxl J., The maximal factorizations of the finite simple groups and their automorphism groups, Mem. Amer. Math. Soc., 86, no. 432, Amer. Math. Soc., Providence, RI, 1990, 151 pp. | MR

[10] Huppert B., Endliche Gruppen I, Grundlehren der mathematischen Wissenschaften, 134, Springer Verlag, Berlin; Heidelberg; NY, 1967, 793 pp. | DOI | MR | Zbl

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

[12] Kleidman P., “The maximal subgroups of the finite 8-dimensional orthogonal groups $P\Omega_8^+(q)$ and their automorphism groups”, J. Algebra, 110:1 (1987), 173–242 | DOI | MR | Zbl

[13] Wilson R.A., The finite simple groups, Grad. Texts in Math., Springer, Berlin; London, 2009, 298 pp. | DOI | MR | Zbl

[14] Bray J.N., Holt D.F., Roney-Douglas C.M., The maximal subgroups of the low-dimensional finite classical groups, Cambridge Univ. Press, Cambridge, 2013, 438 pp. | DOI | MR | Zbl

[15] Suprunenko D.A., Gruppy podstanovok, Navuka i tekhnika, Mn., 1996, 266 pp.

[16] Huppert B., Blackburn N., Finite groups III, Grundlehren der mathematischen Wissenschaften, 243, Springer Verlag, Berlin; Heidelberg; NY, 1982, 454 pp. | DOI | MR | Zbl

[17] Ramanujan S., “A proof of Bertrand's postulate”, J. Indian Math. Soc., 11 (1919), 181–182

[18] Kantor W.M., “Homogeneous designs and geometric lattices”, J. Combinatorian Theory. Ser. A, 38 (1985), 66–74 | DOI | MR | Zbl

[19] Hauck P., Kazarin L., Martinez-Pastor A., Perez-Ramos M.D., “Thompson-like characterization of solubility for products of finite groups”, Ann. Mat. Pura Appl.(4), 200(1) (2021), 337–362 | DOI | MR | Zbl

[20] Kholl M., Teoriya grupp, Izd. inostr. lit., M., 1962, 468 pp.