The eigenvalue one property of finite groups, II

Gerhard Hiß; Rafał Lutowski

doi:10.48550/arxiv.2601.09622

The eigenvalue one property of finite groups, II

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Gerhard Hiß, Rafał Lutowski

DOI: 10.48550/arxiv.2601.09622

Cited by: 0

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.

Fields of Study & Subjects

Geometric and Algebraic Topology Finite Group Theory Research Advanced Algebra and Geometry

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 14 January 2026
Document type: Preprint