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arXiv · 1901.07319

Special $p$-groups acting on compact manifolds

Dávid R. Szabó
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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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Dávid R. Szabó. 2019-12-23. Special $p$-groups acting on compact manifolds. https://arxiv.org/abs/1901.07319

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