The average degree of an irreducible character of a finite group

Isaacs, I. M.; Loukaki, Maria; Moretó, Alexander

doi:10.1007/s11856-013-0013-z

Cited by 33 publications

(26 citation statements)

References 7 publications

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“…We begin the section with the following easy observation, which can be viewed as a p ′ -version of [ILM,Lemma 3.1].…”

Section: Characters Of P ′ -Degree For P > 5 and Solvabilitymentioning

confidence: 99%

Characters of $p’$-degree and Thompson’s character degree theorem

Hưng¹

2017

Rev. Mat. Iberoam.

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Abstract. A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. We obtain a significant improvement of this result by considering the average of p ′ -degrees of irreducible characters. We also consider fields of character values and prove several improvements of earlier related results.

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“…We begin the section with the following easy observation, which can be viewed as a p ′ -version of [ILM,Lemma 3.1].…”

Section: Characters Of P ′ -Degree For P > 5 and Solvabilitymentioning

confidence: 99%

Characters of $p’$-degree and Thompson’s character degree theorem

Hưng¹

2017

Rev. Mat. Iberoam.

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“…In joint work with M. Isaacs and M. Loukaki [3], we proved that if the average character degree of a finite group is ≤ 3 then G is solvable. The main result of this note provides a similar result for the average Sylow number.…”

Section: Introductionmentioning

confidence: 97%

The average number of Sylow subgroups of a finite group

Moretó

2013

Mathematische Nachrichten

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“…For a finite group G, let Irr(G) denote the set of all irreducible (complex) characters of G and acd(G) := 1 |Irr(G)| χ∈Irr (G) χ (1) denote the average character degree of G. Answering affirmatively a question of Berkovich and Zhmud' [3], Magaard and Tong-Viet [12] proved that if acd(G) < 2, then G is solvable. This was improved by Isaacs, Loukaki and Moretó [8] where the hypothesis was weakened to acd(G) < 3. In [8], the authors also obtained the connection between the average character degree and other important characteristics of finite groups such as nilpotency and supersolvability.…”

Section: Introductionmentioning

confidence: 99%

“…This was improved by Isaacs, Loukaki and Moretó [8] where the hypothesis was weakened to acd(G) < 3. In [8], the authors also obtained the connection between the average character degree and other important characteristics of finite groups such as nilpotency and supersolvability. These results demonstrate that the structure of a finite group is somehow controlled by its average character degree.…”

Section: Introductionmentioning

confidence: 99%