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This analysis reveals the relationship between subnormalisers and characters in finite groups, indicating significant findings for unipotent and semisimple elements.
We gather evidence on a new local-global conjecture of Moretó and Rizo on values of irreducible characters of finite groups. For this we study subnormalisers and picky elements in finite groups of Lie type and determine them in many cases, for unipotent elements as well as for semisimple elements of prime power order. We also discuss subnormalisers of unipotent and semisimple elements in connected as well as in disconnected reductive linear algebraic groups.
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Gunter Malle (2025) studied this question.
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