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arXiv · 2408.16785

Zeros of $S$-characters

Thomas Breuer·Michael Joswig·Gunter Malle
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Abstract

The concept of $S$-characters of finite groups was introduced by Zhmud' as a generalisation of transitive permutation characters. Any non-trivial $S$-character takes a zero value on some group element. By a deep result depending on the classification of finite simple groups a non-trivial transitive permutation character even vanishes on some element of prime power order. We present examples that this does not generalise to $S$-characters, thereby answering a question posed by J-P. Serre.

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Thomas Breuer, Michael Joswig, Gunter Malle. 2025-01-06. Zeros of $S$-characters. https://doi.org/10.1016/j.jaca.2025.100031

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