Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS

  • Koo, Daehwan (Daejeon Science High School for the Gifted) ;
  • Oh, Myungsung (Department of Mathematics Education Chungnam National University) ;
  • Shin, Joonkook (Department of Mathematics Education Chungnam National University)
  • Received : 2016.05.31
  • Accepted : 2017.07.03
  • Published : 2017.09.01
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Abstract

We study free actions of finite groups on 3-dimensional nil-manifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

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References

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