On the structure of finite groups with large irreducible character degree $p^2q$
Matematičeskie zametki SVFU, Tome 23 (2016) no. 3, pp. 81-90 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study a finite nontrivial group $G$ with an irreducible complex character $\Theta$ degree $\Theta (1) = p^2q$ such that $|G|\leq 2\Theta (1)^2$, where $p, q$ are primes.
Keywords: finite group, character of a finite group, irreducible character degree of a finite group.
@article{SVFU_2016_23_3_a5,
     author = {S. S. Poiseeva},
     title = {On the structure of finite groups with large irreducible character degree $p^2q$},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {81--90},
     year = {2016},
     volume = {23},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a5/}
}
TY  - JOUR
AU  - S. S. Poiseeva
TI  - On the structure of finite groups with large irreducible character degree $p^2q$
JO  - Matematičeskie zametki SVFU
PY  - 2016
SP  - 81
EP  - 90
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a5/
LA  - ru
ID  - SVFU_2016_23_3_a5
ER  - 
%0 Journal Article
%A S. S. Poiseeva
%T On the structure of finite groups with large irreducible character degree $p^2q$
%J Matematičeskie zametki SVFU
%D 2016
%P 81-90
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a5/
%G ru
%F SVFU_2016_23_3_a5
S. S. Poiseeva. On the structure of finite groups with large irreducible character degree $p^2q$. Matematičeskie zametki SVFU, Tome 23 (2016) no. 3, pp. 81-90. http://geodesic.mathdoc.fr/item/SVFU_2016_23_3_a5/

[1] Poiseeva S. S., “Finite groups with an irreducible character large degree”, Mat. Zamet. SVFU, 22:4 (2015), 43–61 | Zbl

[2] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., Atlas of finite groups: maximal subgroups and ordinary characters for simple groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[3] Kazarin L. S. and Poiseeva S. S, “Finite groups with large irreducible character”, Math. Notes, 98:1 (2015), 265–272 | DOI | DOI | MR | Zbl

[4] Kazarin L. S. and Poiseeva S. S., “On finite groups with large degree irreducible character”, Model. Analiz Inform. Sistem, 22:4 (2015), 483–499 | MR

[5] The GAP Group GAP Groups, Algorithms and Programming, Version 4.4.10, , 2008 http://www.gap-system.org

[6] Zenkov V. I., “About $p$-blocks of defect 0 in $p$-solvable groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 3, 1995, 36–40 | MR | Zbl

[7] Belonogov V. A., Representations and characters of finite groups, Akad. Nauk USSR, Sverdlovsk, 1990 | MR

[8] Feit W., Characters of finite groups, Yale University, New York, Amsterdam, 1967 | MR

[9] Isaacs I. M., Character theory of finite groups, Acad. Press, New York, San Francisco, London, 1976 | MR | Zbl

[10] Guralnick R. M., Malle G., Navarro G., “Self-normalizing Sylow subgroups”, Proc. Amer. Math. Soc, 132:4. (2003), 973–979 | DOI | MR

[11] Zenkov V. I., “The intersections of nilpotent subgroups in finite groups”, Fundam. Prikl. Mat., 2:1 (1996), 1–92 | MR | Zbl