4.5 Article

GROUPS WITH FEW p'-CHARACTER DEGREES IN THE PRINCIPAL BLOCK

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 148, Issue 11, Pages 4597-4614

Publisher

AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15143

Keywords

p'-character degrees; principal block

Funding

  1. Spanish Ministerio de Ciencia e Innovacion [PID2019-103854GB-I00]
  2. FEDER funds
  3. German Research Foundation [SA 2864/1-1, SA 2864/3-1]
  4. National Science Foundation [DMS-1801156]
  5. National Security Agency [H98230-19-1-0119]
  6. Lyda Hill Foundation
  7. McGovern Foundation
  8. Microsoft Research

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Let p >= 5 be a prime and let G be a finite group. We prove that G is p-solvable of p-length at most 2 if there are at most two distinct p'-character degrees in the principal p-block of G. This generalizes a theorem of Isaacs-Smith as well as a recent result of three of the present authors.

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