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J. Korean Math. Soc. 2005; 42(4): 795-826
Printed July 1, 2005
Copyright © The Korean Mathematical Society.
Free actions of finite abelian groups on 3-dimensional nilmanifolds
Dongsoon Choi and Joonkook Shin
Chungnam National University, Chungnam National University
We study free actions of finite abelian groups on $3$-dimensional 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
MSC numbers: Primary 57S25; Secondary 57M05, 57S17
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