DOI: 10.1515/jgth-2022-0215 ISSN: 1433-5883

A characterization of finite groups having a single Galois conjugacy class of certain irreducible characters

Yu Zeng, Dongfang Yang
  • Algebra and Number Theory


Let 𝐺 be a finite group and let

Irr s ( G ) \mathrm{Irr}_{\mathfrak{s}}(G)
be the set of irreducible complex characters 𝜒 of 𝐺 such that
χ ( 1 ) 2 \chi(1)^{2}
does not divide the index of the kernel of 𝜒. In this paper, we classify the finite groups 𝐺 for which any two characters in
Irr s ( G ) \mathrm{Irr}_{\mathfrak{s}}(G)
are Galois conjugate. In particular, we show that such groups are solvable with Fitting height 2.

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