Real Constituents of Permutation Characters
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Publication:6344526
DOI10.1016/J.JALGEBRA.2020.12.017zbMATH Open1510.20010arXiv2007.03026MaRDI QIDQ6344526
Robert Guralnick, Gabriel Navarro
Publication date: 6 July 2020
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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