A NOTE ON DERIVED LENGTH AND CHARACTER DEGREES

Cinarci B., Erkoc T.

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.103, no.2, pp.271-277, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 103 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1017/s0004972720000623
  • Journal Name: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.271-277
  • Keywords: solvable groups, derived length, real and monolithic characters, Taketa inequality, Isaacs-Seitz conjecture
  • Istanbul University Affiliated: Yes

Abstract

Isaacs and Seitz conjectured that the derived length of a finite solvable group G is bounded by the cardinality of the set of all irreducible character degrees of G. We prove that the conjecture holds for G if the degrees of nonlinear monolithic characters of G having the same kernels are distinct. Also, we show that the conjecture is true when G has at most three nonlinear monolithic characters. We give some sufficient conditions for the inequality related to monolithic characters or real-valued irreducible characters of G when the commutator subgroup of G is supersolvable.