M. R. Zinov'eva, V. D. Mazurov, “On finite groups with disconnected prime graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 99–105; Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 139

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 3, Pages 99–105 (Mi timm843)

This article is cited in 17 scientific papers (total in 17 papers)

On finite groups with disconnected prime graph

M. R. Zinov'eva^a, V. D. Mazurov^b

^a Ural Federal University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Full-text PDF (163 kB) Citations (17)

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Abstract: All finite simple nonabelian groups that have the same prime graph as a Frobenius group or a

2

$2$ -Frobenius group are found.

Keywords: finite simple group, prime graph, Frobenius group,

2

$2$ -Frobenius group.

Received: 20.02.2012

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, Volume 283, Issue 1, Pages 139–145
DOI: https://doi.org/10.1134/S0081543813090149

Bibliographic databases:

Document Type: Article

UDC: 512.542

Language: Russian

Citation: M. R. Zinov'eva, V. D. Mazurov, “On finite groups with disconnected prime graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 99–105; Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 139–145

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/timm843

https://www.mathnet.ru/eng/timm/v18/i3/p99

This publication is cited in the following 17 articles:

Guohua Qian, “Finite groups with non-complete character codegree graphs”, Journal of Algebra, 669 (2025), 75
Guohua Qian, “Finite Solvable Groups Whose Prime Graphs have Diameter 3”, Acta. Math. Sin.-English Ser., 41:3 (2025), 975
Andreas Bächle, Ann Kiefer, Sugandha Maheshwary, Ángel del Río, “Gruenberg–Kegel graphs: Cut groups, rational groups and the prime graph question”, Forum Mathematicum, 35:2 (2023), 409
N. V. Maslova, K. A. Il'enko, “On the Coincidence of Gruenberg–Kegel Graphs of an Almost Simple Group and a Nonsolvable Frobenius Group”, Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S130–S135
A. S. Kondrat'ev, N. A. Minigulov, “Finite solvable groups whose Gruenberg-Kegel graphs are isomorphic to the paw”, Tr. IMM UrO RAN, 28, no. 2, 2022, 269–273
Peter J. Cameron, Natalia V. Maslova, “Criterion of unrecognizability of a finite group by its Gruenberg–Kegel graph”, Journal of Algebra, 607 (2022), 186
I. B. Gorshkov, N. V. Maslova, “Finite almost simple groups whose Gruenberg–Kegel graphs coincide with Gruenberg–Kegel graphs of solvable groups”, Algebra and Logic, 57:2 (2018), 115–129
A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010
A. Mohammadzadeh, A. R. Moghaddamfar, “Several quantitative characterizations of some specific groups”, Comment. Math. Univ. Carol., 58:1 (2017), 19–34
N. V. Maslova, D. Pagon, “On the realizability of a graph as the Gruenberg–Kegel graph of a finite group”, Sib. elektron. matem. izv., 13 (2016), 89–100
A. S. Kondrat'ev, “Finite groups with given properties of their prime graphs”, Algebra and Logic, 55:1 (2016), 77–82
A. S. Kondratev, “O konechnykh gruppakh s nebolshim prostym spektrom, II”, Vladikavk. matem. zhurn., 17:2 (2015), 22–31
M. R. Zinov'eva, A. S. Kondrat'ev, “Finite almost simple groups with prime graphs all of whose connected components are cliques”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 178–188
V. D. Mazurov, “ $2$ -Frobenius groups isospectral to the simple group $U_3(3)$ ”, Siberian Math. J., 56:6 (2015), 1108–1113
Ali Mahmoudifar, Behrooz Khosravi, “On quasirecognition by prime graph of the simple groups $A^{+}_{n}(p)$ and $A^{-}_{n}(p)$ ”, J. Algebra Appl., 14:01 (2015), 1550006
Alexander Gruber, Thomas Michael Keller, Mark L. Lewis, Keeley Naughton, Benjamin Strasser, “A characterization of the prime graphs of solvable groups”, Journal of Algebra, 442 (2015), 397
A. L. Gavrilyuk, I. V. Khramtsov, A. S. Kondrat'ev, N. V. Maslova, “On realizability of a graph as the prime graph of a finite group”, Sib. elektron. matem. izv., 11 (2014), 246–257

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