Counterexamples to two conjectures in the Kourovka notebook
Algebra i logika, Tome 58 (2019) no. 3, pp. 370-375.

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

Here we give counterexamples to two conjectures in the [Kourovka Notebook, Quest. 12.78, 19.67; http://www.math.nsc.ru/˜ alglog/19tkt.pdf]. The first conjecture concerns character theory of finite groups, and the second one regards permutation group theory.
Keywords: finite group, character
Mots-clés : permutation group.
@article{AL_2019_58_3_a5,
     author = {S. V. Skresanov},
     title = {Counterexamples to two conjectures in the {Kourovka} notebook},
     journal = {Algebra i logika},
     pages = {370--375},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_3_a5/}
}
TY  - JOUR
AU  - S. V. Skresanov
TI  - Counterexamples to two conjectures in the Kourovka notebook
JO  - Algebra i logika
PY  - 2019
SP  - 370
EP  - 375
VL  - 58
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2019_58_3_a5/
LA  - ru
ID  - AL_2019_58_3_a5
ER  - 
%0 Journal Article
%A S. V. Skresanov
%T Counterexamples to two conjectures in the Kourovka notebook
%J Algebra i logika
%D 2019
%P 370-375
%V 58
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2019_58_3_a5/
%G ru
%F AL_2019_58_3_a5
S. V. Skresanov. Counterexamples to two conjectures in the Kourovka notebook. Algebra i logika, Tome 58 (2019) no. 3, pp. 370-375. http://geodesic.mathdoc.fr/item/AL_2019_58_3_a5/

[1] Unsolved problems in group theory, The Kourovka notebook, 19, Sobolev Institute of Mathematics, Novosibirsk, 2018 http://www.math.nsc.ru/ãlglog/19tkt.pdf

[2] The GAP Group, GAP– Groups, Algorithms, Programming — A System for Computational Discrete Algebra, vers. 4.10.2, , 2019 https://www.gap-system.org

[3] I. M. Isaacs, Character theory of finite groups, Corr. repr. of the 1976 orig., Dover Publ., New York, NY, 1994 | MR | Zbl

[4] M. Larsen, A. Shalev, “Characters of symmetric groups: sharp bounds and applications”, Invent. Math., 174:3 (2008), 645–687 | DOI | MR | Zbl

[5] W. Fulton, J. Harris, Representation theory. A first course, Grad. Texts Math., 129, Springer-Verlag, New York etc, 1991 | MR | Zbl

[6] P. J. Cameron, “Finite permutation groups and finite simple groups”, Bull. Lond. Math. Soc., 13:1 (1981), 1–22 | DOI | MR | Zbl

[7] S. Evdokimov, I. Ponomarenko, “Two-closure of odd permutation group in polynomial time”, Nos. Discrete Math., 235:1–3 (2001), 221–232 | DOI | MR | Zbl