Prime divisors of character degrees

Alexander Moret; Pham Huu Tiep

doi:10.1515/JGT.2008.019

Prime divisors of character degrees

Alexander Moret, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

Pálfy proved that given a solvable group G and a set π of prime divisors of character degrees of G of cardinality at least 3, there exist two different primes p, q ∈ π such that pq divides some character degree. The solvability hypothesis cannot be removed from Pálfys theorem, but we show that the same conclusion holds for arbitrary finite groups if |π| ≥ 4.

Original language	English (US)
Pages (from-to)	341-356
Number of pages	16
Journal	Journal of Group Theory
Volume	11
Issue number	3
DOIs	https://doi.org/10.1515/JGT.2008.019
State	Published - May 2008

ASJC Scopus subject areas

Algebra and Number Theory

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10.1515/JGT.2008.019

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title = "Prime divisors of character degrees",

abstract = "P{\'a}lfy proved that given a solvable group G and a set π of prime divisors of character degrees of G of cardinality at least 3, there exist two different primes p, q ∈ π such that pq divides some character degree. The solvability hypothesis cannot be removed from P{\'a}lfys theorem, but we show that the same conclusion holds for arbitrary finite groups if |π| ≥ 4.",

author = "Alexander Moret and Tiep, {Pham Huu}",

note = "Funding Information: The first author is partially supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia, the FEDER, the Generalitat Valenciana and the Programa Ram{\'o}n y Cajal. The second author gratefully acknowledges the support of the NSA (grant H98230-04-0066) and the NSF (grant DMS-0600967).",

year = "2008",

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doi = "10.1515/JGT.2008.019",

language = "English (US)",

volume = "11",

pages = "341--356",

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T1 - Prime divisors of character degrees

AU - Moret, Alexander

AU - Tiep, Pham Huu

N1 - Funding Information: The first author is partially supported by the Spanish Ministerio de Educación y Ciencia, the FEDER, the Generalitat Valenciana and the Programa Ramón y Cajal. The second author gratefully acknowledges the support of the NSA (grant H98230-04-0066) and the NSF (grant DMS-0600967).

PY - 2008/5

Y1 - 2008/5

N2 - Pálfy proved that given a solvable group G and a set π of prime divisors of character degrees of G of cardinality at least 3, there exist two different primes p, q ∈ π such that pq divides some character degree. The solvability hypothesis cannot be removed from Pálfys theorem, but we show that the same conclusion holds for arbitrary finite groups if |π| ≥ 4.

AB - Pálfy proved that given a solvable group G and a set π of prime divisors of character degrees of G of cardinality at least 3, there exist two different primes p, q ∈ π such that pq divides some character degree. The solvability hypothesis cannot be removed from Pálfys theorem, but we show that the same conclusion holds for arbitrary finite groups if |π| ≥ 4.

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DO - 10.1515/JGT.2008.019

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JO - Journal of Group Theory

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ER -

Prime divisors of character degrees

Abstract

ASJC Scopus subject areas

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