Standard

On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”. / Zenkov, V.
в: Proceedings of the Steklov Institute of Mathematics, Том 323, № S1, 01.12.2023, стр. S321-S332.

Результаты исследований: Вклад в журнал › Статья › Рецензирование

Harvard

Zenkov, V 2023, 'On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”', Proceedings of the Steklov Institute of Mathematics, Том. 323, № S1, стр. S321-S332. https://doi.org/10.1134/S0081543823060251

APA

Zenkov, V. (2023). On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”. Proceedings of the Steklov Institute of Mathematics, 323(S1), S321-S332. https://doi.org/10.1134/S0081543823060251

Vancouver

Zenkov V. On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”. Proceedings of the Steklov Institute of Mathematics. 2023 дек. 1;323(S1):S321-S332. doi: 10.1134/S0081543823060251

Author

Zenkov, V. / On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”. в: Proceedings of the Steklov Institute of Mathematics. 2023 ; Том 323, № S1. стр. S321-S332.

BibTeX

@article{ad9d66f9218142a69a7d8df53e2fffeb,
title = "On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”",
abstract = "Earlier, the author described up to conjugacy all pairs AB of nilpotent subgroups of a finite group G with socle L2(q) for which AsuperscriptBg1 for any element of G. A similar description was obtained by the author later for primary subgroups A and B of a finite group G with socle Ln(2m). In this paper, we describe up to conjugacy all pairs AB of nilpotent subgroups of a finite group G with simple socle from the “Atlas of Finite Groups” for which AsuperscriptBg1 for any element g of G. The results obtained in the considered cases confirm the hypothesis (Problem 15.40 from the “Kourovka Notebook”) that a finite simple nonabelian group G for any nilpotent subgroups N contains an element g such that N ∩ Ng=1.",
author = "V. Zenkov",
note = "This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00456).",
year = "2023",
month = dec,
day = "1",
doi = "10.1134/S0081543823060251",
language = "English",
volume = "323",
pages = "S321--S332",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "Pleiades Publishing",
number = "S1",

}

RIS

TY - JOUR

T1 - On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups”

AU - Zenkov, V.

N1 - This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00456).

PY - 2023/12/1

Y1 - 2023/12/1

N2 - Earlier, the author described up to conjugacy all pairs AB of nilpotent subgroups of a finite group G with socle L2(q) for which AsuperscriptBg1 for any element of G. A similar description was obtained by the author later for primary subgroups A and B of a finite group G with socle Ln(2m). In this paper, we describe up to conjugacy all pairs AB of nilpotent subgroups of a finite group G with simple socle from the “Atlas of Finite Groups” for which AsuperscriptBg1 for any element g of G. The results obtained in the considered cases confirm the hypothesis (Problem 15.40 from the “Kourovka Notebook”) that a finite simple nonabelian group G for any nilpotent subgroups N contains an element g such that N ∩ Ng=1.

AB - Earlier, the author described up to conjugacy all pairs AB of nilpotent subgroups of a finite group G with socle L2(q) for which AsuperscriptBg1 for any element of G. A similar description was obtained by the author later for primary subgroups A and B of a finite group G with socle Ln(2m). In this paper, we describe up to conjugacy all pairs AB of nilpotent subgroups of a finite group G with simple socle from the “Atlas of Finite Groups” for which AsuperscriptBg1 for any element g of G. The results obtained in the considered cases confirm the hypothesis (Problem 15.40 from the “Kourovka Notebook”) that a finite simple nonabelian group G for any nilpotent subgroups N contains an element g such that N ∩ Ng=1.

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U2 - 10.1134/S0081543823060251

DO - 10.1134/S0081543823060251

M3 - Article

VL - 323

SP - S321-S332

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - S1

ER -

ID: 53790958