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The Strong π-Sylow Theorem for the Groups PSL. / Revin, D. O.; Shepelev, V. D.

In: Siberian Mathematical Journal, Vol. 65, No. 5, 09.2024, p. 1187-1194.

Research output: Contribution to journal › Article › peer-review

Harvard

Revin, DO & Shepelev, VD 2024, 'The Strong π-Sylow Theorem for the Groups PSL', Siberian Mathematical Journal, vol. 65, no. 5, pp. 1187-1194. https://doi.org/10.1134/S0037446624050173

APA

Revin, D. O., & Shepelev, V. D. (2024). The Strong π-Sylow Theorem for the Groups PSL. Siberian Mathematical Journal, 65(5), 1187-1194. https://doi.org/10.1134/S0037446624050173

Vancouver

Revin DO, Shepelev VD. The Strong π-Sylow Theorem for the Groups PSL. Siberian Mathematical Journal. 2024 Sept;65(5):1187-1194. doi: 10.1134/S0037446624050173

Author

Revin, D. O. ; Shepelev, V. D. / The Strong π-Sylow Theorem for the Groups PSL. In: Siberian Mathematical Journal. 2024 ; Vol. 65, No. 5. pp. 1187-1194.

BibTeX

@article{2a69e319b80d4593af5b84fb9ddffe50,
title = "The Strong π-Sylow Theorem for the Groups PSL",
abstract = "Let π be a set of primes. A finite group G is a π-group if all prime divisors of the order of G belong to π. Following Wielandt, the π-Sylow theorem holds for G if all maximal π-subgroups of G are conjugate; if the π-Sylow theorem holds for every subgroup of G then the strong π-Sylow theorem holds for G. The strong π-Sylow theorem is known to hold for G if and only if it holds for every nonabelian composition factor of G. In 1979, Wielandt asked which finite simple nonabelian groups obey the strong π-Sylow theorem. By now the answer is known for sporadic and alternating groups. We give some arithmetic criterion for the validity of the strong π-Sylow theorem for the groups PSL2(q).",
keywords = "-Sylow theorem, 512.542, projective special linear group, strong -Sylow theorem",
author = "Revin, {D. O.} and Shepelev, {V. D.}",
note = "The research was supported by the Russian Science Foundation (Project 24–21–00163), https://rscf.ru/project/24-21-00163/.",
year = "2024",
month = sep,
doi = "10.1134/S0037446624050173",
language = "English",
volume = "65",
pages = "1187--1194",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "5",

}

RIS

TY - JOUR

T1 - The Strong π-Sylow Theorem for the Groups PSL

AU - Revin, D. O.

AU - Shepelev, V. D.

N1 - The research was supported by the Russian Science Foundation (Project 24–21–00163), https://rscf.ru/project/24-21-00163/.

PY - 2024/9

Y1 - 2024/9

N2 - Let π be a set of primes. A finite group G is a π-group if all prime divisors of the order of G belong to π. Following Wielandt, the π-Sylow theorem holds for G if all maximal π-subgroups of G are conjugate; if the π-Sylow theorem holds for every subgroup of G then the strong π-Sylow theorem holds for G. The strong π-Sylow theorem is known to hold for G if and only if it holds for every nonabelian composition factor of G. In 1979, Wielandt asked which finite simple nonabelian groups obey the strong π-Sylow theorem. By now the answer is known for sporadic and alternating groups. We give some arithmetic criterion for the validity of the strong π-Sylow theorem for the groups PSL2(q).

AB - Let π be a set of primes. A finite group G is a π-group if all prime divisors of the order of G belong to π. Following Wielandt, the π-Sylow theorem holds for G if all maximal π-subgroups of G are conjugate; if the π-Sylow theorem holds for every subgroup of G then the strong π-Sylow theorem holds for G. The strong π-Sylow theorem is known to hold for G if and only if it holds for every nonabelian composition factor of G. In 1979, Wielandt asked which finite simple nonabelian groups obey the strong π-Sylow theorem. By now the answer is known for sporadic and alternating groups. We give some arithmetic criterion for the validity of the strong π-Sylow theorem for the groups PSL2(q).

KW - -Sylow theorem

KW - 512.542

KW - projective special linear group

KW - strong -Sylow theorem

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85204874304&origin=inward&txGid=313f62165d77d77080b9a13bc0564d97

UR - https://elibrary.ru/item.asp?id=69920893

UR - https://www.mendeley.com/catalogue/d880aedd-19e0-3815-be2f-7b57297b1e87/

U2 - 10.1134/S0037446624050173

DO - 10.1134/S0037446624050173

M3 - Article

VL - 65

SP - 1187

EP - 1194

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -

ID: 60797873