P-parts of character degrees

Mark L. Lewis, Gabriel Navarro, Pham Huu Tiep, Hung P. Tong-Viet

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We show that if p is an odd prime and G is a finite group satisfying the condition that p2 divides the degree of no irreducible character of G, then /G: Op(G)/p ≤ p4, where Op(G) is the largest normal p-subgroup of G, and if P is a Sylow p-subgroup of G, then P″ is subnormal in G. Our investigations suggest that if pa is the largest power of p dividing the degrees of irreducible characters of G, then /G: Op(G)/p is bounded by pf(a), where f (a) is a function in a and P(a+1) is subnormal in G.

Original languageEnglish (US)
Pages (from-to)483-497
Number of pages15
JournalJournal of the London Mathematical Society
Volume92
Issue number2
DOIs
StatePublished - Nov 20 2014

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Character Degrees
Irreducible Character
Subgroup
Divides
Finite Group
Odd

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

P-parts of character degrees. / Lewis, Mark L.; Navarro, Gabriel; Tiep, Pham Huu; Tong-Viet, Hung P.

In: Journal of the London Mathematical Society, Vol. 92, No. 2, 20.11.2014, p. 483-497.

Research output: Contribution to journalArticle

Lewis, ML, Navarro, G, Tiep, PH & Tong-Viet, HP 2014, 'P-parts of character degrees', Journal of the London Mathematical Society, vol. 92, no. 2, pp. 483-497. https://doi.org/10.1112/jlms/jdv035
Lewis, Mark L. ; Navarro, Gabriel ; Tiep, Pham Huu ; Tong-Viet, Hung P. / P-parts of character degrees. In: Journal of the London Mathematical Society. 2014 ; Vol. 92, No. 2. pp. 483-497.
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