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http://dx.doi.org/10.4134/JKMS.j160394

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)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1411-1440 More about this Journal
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.
Keywords
affine conjugacy; almost Bieberbach group; group action; Heisenberg group;
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Times Cited By KSCI : 3  (Citation Analysis)
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