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arxiv: 1905.07431 · v1 · pith:P5F6IGD6new · submitted 2019-05-17 · 🧮 math.GR

Rational Groups and a Characterization of a Class of Permutation Groups

Cecil Andrew Ellard This is my paper
classification 🧮 math.GR
keywords grouppermutationrationalfinitegroupsonlycharacterizationcharacters
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We prove that a finite group is rational if and only if it has a set of permutation characters which separate conjugacy classes. It follows from this that a finite group is rational if and only if it has a representation as a permutation group in which any two elements fixing the same number of letters are conjugate.

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