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http://dx.doi.org/10.4134/JKMS.2005.42.4.795

FREE ACTIONS OF FINITE ABELIAN GROUPS ON 3-DIMENSIONAL NILMANIFOLDS  

Choi, Dong-Soon (Department of Mathematics Chungnam National University)
Shin, Joon-Kook (Department of Mathematics Chungnam National University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.4, 2005 , pp. 795-826 More about this Journal
Abstract
We study free actions of finite abelian groups on 3­dimensional nilmanifolds. 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. All such actions are completely classified.
Keywords
group actions; Heisenberg group; almost Bieberbach groups; Affine conjugacy;
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