The eigenvalue one property of finite groups, I

Gerhard Hiss; Rafał Lutowski

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arXiv · 2504.04978

The eigenvalue one property of finite groups, I

Gerhard Hiss·Rafał Lutowski

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Abstract

We prove a conjecture of Dekimpe, De Rock and Penninckx concerning the existence of eigenvalues one in certain elements of finite groups acting irreducibly on a real vector space of odd dimension. This yields a sufficient condition for a closed flat manifold to be an $R_{\infty}$-manifold.

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Gerhard Hiss, Rafał Lutowski. 2025-04-07. The eigenvalue one property of finite groups, I. https://arxiv.org/abs/2504.04978

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