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This article is cited in 20 scientific papers (total in 20 papers)
Recognizability of alternating groups by spectrum
I. B. Gorshkov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract:
The spectrum of a group is the set of its element orders. A finite group $G$ is said to be recognizable by spectrum if every finite group that has the same spectrum as $G$ is isomorphic to $G$. It is proved that simple alternating groups An are recognizable by spectrum, for $n\ne6,10$. This implies that every finite group whose spectrum coincides with that of a finite non-Abelian simple group has at most one non-Abelian composition factor.
Keywords:
finite group, simple group, alternating group, spectrum of group, recognizability by spectrum.
Received: 18.07.2012 Revised: 04.12.2012
Citation:
I. B. Gorshkov, “Recognizability of alternating groups by spectrum”, Algebra Logika, 52:1 (2013), 57–63; Algebra and Logic, 52:1 (2013), 41–45
Linking options:
https://www.mathnet.ru/eng/al571 https://www.mathnet.ru/eng/al/v52/i1/p57
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Abstract page: | 453 | Full-text PDF : | 126 | References: | 66 | First page: | 33 |
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