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<p>The celebrated Itô–Michler theorem asserts that a prime <i>p</i> does not divide the degree of any irreducible character of a finite group <i>G</i> if and only if <i>G</i> has a normal and abelian Sylow <i>p</i>-subgroup. The principal block case of the recently-proven Brauer’s height zero conjecture isolates the abelian part in the Itô–Michler theorem. In this paper, we show that the normal part can also be isolated in a similar way. This is a consequence of work on a strong form of the so-called Brauer’s height zero conjecture for two primes of Malle and Navarro. Using our techniques, we also provide an alternate proof of this conjecture.</p>

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A normal version of Brauer’s height zero conjecture

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月17日

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  • Alexander Moretó,
  • A. A. Schaeffer Fry

摘要

The celebrated Itô–Michler theorem asserts that a prime p does not divide the degree of any irreducible character of a finite group G if and only if G has a normal and abelian Sylow p-subgroup. The principal block case of the recently-proven Brauer’s height zero conjecture isolates the abelian part in the Itô–Michler theorem. In this paper, we show that the normal part can also be isolated in a similar way. This is a consequence of work on a strong form of the so-called Brauer’s height zero conjecture for two primes of Malle and Navarro. Using our techniques, we also provide an alternate proof of this conjecture.