Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2017; 54(5): 1411-1440

Online first article August 18, 2017      Printed September 1, 2017

https://doi.org/10.4134/JKMS.j160394

Copyright © The Korean Mathematical Society.

Classification of free actions of finite groups on 3-dimensional nilmanifolds

Daehwan Koo, Myungsung Oh, and Joonkook Shin

Daejeon Science High School for the Gifted, Chungnam National University, Chungnam National University

Abstract

We study free actions of finite groups on 3-dimensional nilmanifolds with the first homology $\bz^2\oplus \bz_p$. 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

MSC numbers: Primary 57S25; Secondary 57M05, 57S17