FREE ACTIONS OF FINITE ABELIAN GROUPS ON 3-DIMENSIONAL NILMANIFOLDS Choi, Dong-Soon; Shin, Joon-Kook;
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.
group actions;Heisenberg group;almost Bieberbach groups;Affine conjugacy;