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This article is cited in 1 scientific paper (total in 1 paper)
Recognizability of symmetric groups by spectrum
I. B. Gorshkov Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
Abstract:
The spectrum of a finite group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group whose spectrum coincides with the spectrum of $G$ is isomorphic to $G$. It is proved the symmetric group $S_n$ is recognizable by spectrum for $n\not\in\{2,3,4,5,6,8,10,15,16,18,21,27,33,35,39,45\}$.
Keywords:
finite group, simple group, symmetric group, spectrum of group, recognition by spectrum.
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English version:
Algebra and Logic, 2015, 53:6, 450–457
Bibliographic databases:
UDC:
512.542 Received: 23.04.2014
Citation:
I. B. Gorshkov, “Recognizability of symmetric groups by spectrum”, Algebra Logika, 53:6 (2014), 693–703; Algebra and Logic, 53:6 (2015), 450–457
Citation in format AMSBIB
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\pages 693--703
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http://mi.mathnet.ru/eng/al660 http://mi.mathnet.ru/eng/al/v53/i6/p693
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This publication is cited in the following articles:
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I. B. Gorshkov, A. N. Grishkov, “On recognition by spectrum of symmetric groups”, Sib. elektron. matem. izv., 13 (2016), 111–121
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