Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS WITH HOMOTOPICALLY TRIVIAL TRANSLATIONS

  • Koo, Daehwan (Daejeon Science High School for the Gifted) ;
  • Park, Eunmi (Daejeon Foreign Language High School) ;
  • Shin, Joonkook (Department of Mathematics Education Chungnam National University)
  • Received : 2020.01.08
  • Accepted : 2020.01.29
  • Published : 2020.02.15
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Abstract

We show that if a finite group G acts freely with homotopically trivial translations on a 3-dimensional nilmanifold 𝓝p with the first homology ℤ2 ⊕ ℤp, then either G is cyclic or there exist finite nonabelian groups acting freely on 𝓝p which yield orbit manifolds homeomorphic to 𝓝/𝜋3 or 𝓝/𝜋4.

Keywords

Acknowledgement

This study was financially supported by Research Fund of Chungnam National University.

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