Some special coprime actions and their consequences

ERCAN G., Güloğlu İ. Ş., Kizmaz M. Y., Revin D. O.

Journal of Pure and Applied Algebra, cilt.228, sa.12, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 228 Sayı: 12
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.jpaa.2024.107764
  • Dergi Adı: Journal of Pure and Applied Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Coprime action, Fitting series, Frobenius action, p-length, Simple group
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup CG(A) is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.