CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS

CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS

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...

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Veröffentlicht in:Journal of the Korean Mathematical Society 2017, Vol.54 (5), p.1411-1440
Hauptverfasser: Koo, Daehwan, Oh, Myungsung, Shin, Joonkook
Format: Artikel
Sprache:kor
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Zusammenfassung: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.
ISSN:0304-9914