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On groups having the prime graph as alternating and symmetric groups. / Gorshkov, Ilya; Staroletov, Alexey.

In: Communications in Algebra, Vol. 47, No. 9, 02.09.2019, p. 3905-3914.

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

Harvard

Gorshkov, I & Staroletov, A 2019, 'On groups having the prime graph as alternating and symmetric groups', Communications in Algebra, vol. 47, no. 9, pp. 3905-3914. https://doi.org/10.1080/00927872.2019.1572167

APA

Gorshkov, I., & Staroletov, A. (2019). On groups having the prime graph as alternating and symmetric groups. Communications in Algebra, 47(9), 3905-3914. https://doi.org/10.1080/00927872.2019.1572167

Vancouver

Gorshkov I, Staroletov A. On groups having the prime graph as alternating and symmetric groups. Communications in Algebra. 2019 Sept 2;47(9):3905-3914. doi: 10.1080/00927872.2019.1572167

Author

Gorshkov, Ilya ; Staroletov, Alexey. / On groups having the prime graph as alternating and symmetric groups. In: Communications in Algebra. 2019 ; Vol. 47, No. 9. pp. 3905-3914.

BibTeX

@article{1ec876695ae541ee98053928706e3b53,
title = "On groups having the prime graph as alternating and symmetric groups",
abstract = " The prime graph Γ(G) of a finite group G is the graph whose vertex set is the set of prime divisors of |G| and in which two distinct vertices r and s are adjacent if and only if there exists an element of G of order rs. Let A n (S n ) denote the alternating (symmetric) group of degree n. We prove that if G is a finite group with Γ(G)=Γ(A n ) or Γ(G)=Γ(S n ), where n≥19, then there exists a normal subgroup K of G and an integer t such that A t ≤G(K)≤S t and |K| is divisible by at most one prime greater than n/2. ",
keywords = "alternating groups, finite simple groups, Prime graph, symmetric groups, FINITE, RECOGNITION, RECOGNIZABILITY",
author = "Ilya Gorshkov and Alexey Staroletov",
note = "Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Taylor & Francis Group, LLC.",
year = "2019",
month = sep,
day = "2",
doi = "10.1080/00927872.2019.1572167",
language = "English",
volume = "47",
pages = "3905--3914",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "9",

}

RIS

TY - JOUR

T1 - On groups having the prime graph as alternating and symmetric groups

AU - Gorshkov, Ilya

AU - Staroletov, Alexey

N1 - Publisher Copyright: © 2019, © 2019 Taylor & Francis Group, LLC.

PY - 2019/9/2

Y1 - 2019/9/2

N2 - The prime graph Γ(G) of a finite group G is the graph whose vertex set is the set of prime divisors of |G| and in which two distinct vertices r and s are adjacent if and only if there exists an element of G of order rs. Let A n (S n ) denote the alternating (symmetric) group of degree n. We prove that if G is a finite group with Γ(G)=Γ(A n ) or Γ(G)=Γ(S n ), where n≥19, then there exists a normal subgroup K of G and an integer t such that A t ≤G(K)≤S t and |K| is divisible by at most one prime greater than n/2.

AB - The prime graph Γ(G) of a finite group G is the graph whose vertex set is the set of prime divisors of |G| and in which two distinct vertices r and s are adjacent if and only if there exists an element of G of order rs. Let A n (S n ) denote the alternating (symmetric) group of degree n. We prove that if G is a finite group with Γ(G)=Γ(A n ) or Γ(G)=Γ(S n ), where n≥19, then there exists a normal subgroup K of G and an integer t such that A t ≤G(K)≤S t and |K| is divisible by at most one prime greater than n/2.

KW - alternating groups

KW - finite simple groups

KW - Prime graph

KW - symmetric groups

KW - FINITE

KW - RECOGNITION

KW - RECOGNIZABILITY

UR - http://www.scopus.com/inward/record.url?scp=85063520547&partnerID=8YFLogxK

U2 - 10.1080/00927872.2019.1572167

DO - 10.1080/00927872.2019.1572167

M3 - Article

AN - SCOPUS:85063520547

VL - 47

SP - 3905

EP - 3914

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 9

ER -

ID: 19039664