Special p-groups acting on compact manifolds

2019/01/22 by Dávid R. Szabó, Szabó, Dávid R. · 1 citation
Mathematics · #20D15 #54H15 #57S17 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1901.07319

openalex publication_date 2019/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Riera proved at arXiv:1412.6964 that the diffeomorphism group of particular compact manifolds are not Jordan by exhibiting subgroups isomorphic to extra-special p-groups of exponent p for primes p satisfying some conditions. Generalising the methods of that paper, we construct a compact connected smooth real manifold for every natural number r whose diffeomorphism group contains not only every extra-special p-group, but also every special p-group of order p^r independently of its exponent for every prime p. We obtain a similar statement about finite Heisenberg groups as well as we display a very explicit counterexample to the conjecture of Ghys about Jordan property of diffeomorphism group of compact manifolds.

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