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The Taketa Problem and Character Degree Graphs with Diameter Three

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Let G be a solvable group and let Δ(G) be the character degree graph of G. The vertices of Δ(G) are the primes dividing character degrees of G and there is an edge between two primes if they divide a common character degree of G. In this paper, we show that the Taketa inequality dl(G) ≤ | cd(G)| holds when G is a solvable group whose degree graph Δ(G) has diameter 3.

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Correspondence to Mark L. Lewis.

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Presented by Radha Kessar.

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Lewis, M.L., Sass, C.B. The Taketa Problem and Character Degree Graphs with Diameter Three. Algebr Represent Theor 18, 1395–1399 (2015).

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Mathematics Subject Classification (2010)