Groups with just one character degree divisible by a given prime

I. M. Isaacs, Alexander Moretó, Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.

Original languageEnglish (US)
Pages (from-to)6521-6547
Number of pages27
JournalTransactions of the American Mathematical Society
Volume361
Issue number12
DOIs
StatePublished - Dec 2009

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Character Degrees
Irreducible Character
Divisible
Subgroup
Finite Group
Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Groups with just one character degree divisible by a given prime. / Isaacs, I. M.; Moretó, Alexander; Navarro, Gabriel; Tiep, Pham Huu.

In: Transactions of the American Mathematical Society, Vol. 361, No. 12, 12.2009, p. 6521-6547.

Research output: Contribution to journalArticle

Isaacs, I. M. ; Moretó, Alexander ; Navarro, Gabriel ; Tiep, Pham Huu. / Groups with just one character degree divisible by a given prime. In: Transactions of the American Mathematical Society. 2009 ; Vol. 361, No. 12. pp. 6521-6547.
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