For dihedral groups D_n, T(D_n) ≥ m_σ holds for every automorphism σ, with m_σ classified via number-theoretic properties of the automorphism parameters.
Gow,Properties of the characters of the finite general linear group related to the transpose- inverse involution, Proc
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Twisted Frobenius-Schur Indicators and Character Degree Sums in Dihedral Groups
For dihedral groups D_n, T(D_n) ≥ m_σ holds for every automorphism σ, with m_σ classified via number-theoretic properties of the automorphism parameters.