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arxiv: 1901.06297 · v1 · pith:2EKQVODWnew · submitted 2019-01-18 · 🧮 math.GR · math.RT

Frobenius-Schur indicators of characters in blocks with cyclic defect

classification 🧮 math.GR math.RT
keywords charactersfrobenius-schurcyclicindicatorsdefectfinitegroupindicator
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Let $p$ be an odd prime and let $B$ be a $p$-block of a finite group which has cyclic defect groups. We show that all exceptional characters in $B$ have the same Frobenius-Schur indicators. Moreover the common indicator can be computed, using the canonical character of $B$. We also investigate the Frobenius-Schur indicators of the non-exceptional characters in $B$. For a finite group which has cyclic Sylow $p$-subgroups, we show that the number of irreducible characters with Frobenius-Schur indicator $-1$ is greater than or equal to the number of conjugacy classes of weakly real $p$-elements in $G$.

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