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We show that the Igusa-Klein topological torsion and the Bismut-Lott analytictorsion are equivalent for any flat vector bundle whose holonomy is a finitesubgroup of $\mathrm{GL}_n(\mathbb{Q})$. Our proof uses Artin's inductiontheorem in representation theory to reduce the problem to the special case oftrivial flat line bundles, which is a recent result of Puchol, Zhu and thesecond author. The idea of using Artin's induction theorem appeared in a paperof Ohrt on the same topic, of which our present work is an improvement.

A remark on the higher torsion invariants for flat vector bundles with finite holonomy