Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups

Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups

It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no 3-cocliques....

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Veröffentlicht in:Algebra and logic 2018-06, Vol.57 (2), p.115-129
Hauptverfasser: Gorshkov, I. B., Maslova, N. V.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Graph theory
Graphs
Groups (Mathematics)
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Zusammenfassung:It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no 3-cocliques.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-018-9484-7