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Scholars Journal of Physics, Mathematics and Statistics | Volume-11 | Issue-01
Galois Conjugacy and Fitting Height 2: Classification of Finite Solvable Groups
Michael N. John, Eno John, Enyiduru, Ekwomchi Hannah, Otobong J. Tom
Published: Jan. 20, 2024 | 163 136
DOI: 10.36347/sjpms.2024.v11i01.002
Pages: 6-10
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Abstract
This paper investigates the finite groups 𝐺 for which any two characters in the set of irreducible complex characters 𝑰𝒓𝒓(𝐺) are Galois conjugate. Specifically, we classify such groups and establish a key result: they are solvable with Fitting height 2. The analysis involves intricate considerations of irreducible complex characters and their Galois conjugacy, shedding light on the structural properties of finite solvable groups.