A NOTE ON DERIVED LENGTH AND CHARACTER DEGREES
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, cilt.103, sa.2, ss.271-277, 2021 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 103 Sayı: 2
- Basım Tarihi: 2021
- Doi Numarası: 10.1017/s0004972720000623
- Dergi Adı: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
- Sayfa Sayıları: ss.271-277
- Anahtar Kelimeler: solvable groups, derived length, real and monolithic characters, Taketa inequality, Isaacs-Seitz conjecture
- İstanbul Üniversitesi Adresli: Evet
Özet
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.