P-parts of character degrees

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

Research output: Contribution to journalArticle

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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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ASJC Scopus subject areas

  • Mathematics(all)

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