Some special coprime actions and their consequences


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

Journal of Pure and Applied Algebra, vol.228, no.12, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 228 Issue: 12
  • Publication Date: 2024
  • Doi Number: 10.1016/j.jpaa.2024.107764
  • Journal Name: Journal of Pure and Applied Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Keywords: Coprime action, Fitting series, Frobenius action, p-length, Simple group
  • Middle East Technical University Affiliated: Yes

Abstract

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.