Rational Groups and a Characterization of a Class of Permutation Groups

Cecil Andrew Ellard

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arXiv · 1905.07431

Rational Groups and a Characterization of a Class of Permutation Groups

Cecil Andrew Ellard

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Abstract

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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Cecil Andrew Ellard. 2019-05-17. Rational Groups and a Characterization of a Class of Permutation Groups. https://arxiv.org/abs/1905.07431

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