Treffer: Diameters of degree graphs of nonsolvable groups: Diameters of degree graphs of nonsolvable groups.

Title:
Diameters of degree graphs of nonsolvable groups: Diameters of degree graphs of nonsolvable groups.
Authors:
Donald L. White, Mark L. Lewis
Source:
Journal of Algebra. 283:80-92
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Subject Terms:
Degree graphs, Ordinary representations and characters, first Janko group, Algebra and Number Theory, 01 natural sciences, Character degrees, Graphs and abstract algebra (groups, rings, fields, etc.), diameters, irreducible complex characters, character degree graphs, Nonsolvable groups, 0101 mathematics, Representations of sporadic groups, Arithmetic and combinatorial problems involving abstract finite groups
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
0021-8693
DOI:
10.1016/j.jalgebra.2004.08.025
DOI:
10.1016/j.jalgebra.2007.02.057
Access URL:
https://core.ac.uk/display/82828386
https://www.sciencedirect.com/science/article/pii/S0021869304004855
https://www.sciencedirect.com/science/article/abs/pii/S0021869307002037
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....537d70b2d85c5ee0b6c200d6f1b7fe4e
Database:
OpenAIRE

Weitere Informationen

Let \(G\) be a finite group. The character degree graph \(\Delta(G)\) is the graph whose vertices are the primes dividing at least one irreducible complex character degree of \(G\) and whose edges are between primes whose product divides at least one such degree. This graph has been studied in quite some detail in the recent past. In the paper under review, the authors are concerned with the diameter of \(\Delta(G)\) (which is the maximum of the diameters of the connected components of \(\Delta(G)\)). They prove that it is bounded above by 2 for nonabelian finite simple groups, except for the Janko group \(J_1\), for which it is 3. They also prove that for an arbitrary finite group the diameter is bounded above by 4; they conjecture, however, that 3 is the best possible upper bound.