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arXiv · 2007.03026

Real Constituents of Permutation Characters

Robert Guralnick·Gabriel Navarro
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Abstract

We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple Groups). Along the way, we also give a new characterization of the 2-closed finite groups using odd-order real elements of the group. All this can be seen as a contribution to Brauer's Problem 11. We also obtain similar results for 2-Brauer characters. We also classify finite primitive permutation groups in which every real element has a fixed point.

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Robert Guralnick, Gabriel Navarro. 2021-01-07. Real Constituents of Permutation Characters. https://arxiv.org/abs/2007.03026

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