Characterization of A₁₆ by a noncommuting graph
Let G be a finite non-Abelian group. We define a graph Γ G ; called the noncommuting graph of G; with a vertex set G − Z(G) such that two vertices x and y are adjacent if and only if xy ≠ yx: Abdollahi, Akbari, and Maimani put forward the following conjecture (the AAM conjecture): If S is a finite n...
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| Datum: | 2010 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2010
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| Schriftenreihe: | Український математичний журнал |
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| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/166289 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Characterization of A₁₆ by a noncommuting graph / M. Davoudi Monfared, M.R. Darafsheh // Український математичний журнал. — 2010. — Т. 62, № 11. — С. 1443–1450. — Бібліогр.: 12 назв. — укр. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let G be a finite non-Abelian group. We define a graph Γ G ; called the noncommuting graph of G; with a vertex set G − Z(G) such that two vertices x and y are adjacent if and only if xy ≠ yx: Abdollahi, Akbari, and Maimani put forward the following conjecture (the AAM conjecture): If S is a finite non-Abelian simple group and G is a group such that Γ S ≅ Γ G ; then S ≅ G: It is still unknown if this conjecture holds for all simple finite groups with connected prime graph except A₁₀, L₄(8), L₄(4), and U₄(4). In this paper, we prove that if A₁₆ denotes the alternating group of degree 16; then, for any finite group G; the graph isomorphism ΓA₁₆≅ΓG implies that A₁₆≅G. |
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