• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1411-1440
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• 2017

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.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.161-175
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• 1997

We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1065-1080
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• 2006

For 3-dimensional Bieberbach groups, we study the de-formation spaces in the group of isometries of $R^3$. First we calculate the discrete representation spaces and the automorphism groups. Then for each of these Bieberbach groups, we give complete descriptions of $Teichm\ddot{u}ller$ spaces, Chabauty spaces, and moduli spaces.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.795-826
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• 2005

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.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.2
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• pp.27-35
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• 2001

We shall deal with ten cases out of 15 distinct almost Bieberbach groups up to Seifert local invariant. In those cases we will show that if G is a finite abelian group acting freely on the standard nilmanifold, then G is cyclic, up to topological conjugacy.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.285-287
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• 2019

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.437-443
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• 2006

We study free actions of finite groups on the 3-dimensional nilmanifold for Type 1 and classify all such group actions, up to topological conjugacy. This work supplies missing one in [1, Theorem 3.11.].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.223-230
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• 2007

We study free actions of finite groups on the 3-dimensional nilmanifold and classify all such group actions, up to topological conjugacy. This work generalize Theorem 3.10 of [1].

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.223-232
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• 2005

We study only free actions of finite groups G on the 3-dimensional nilmanifold, up to topological conjugacy which yields an infra-nilmanifold of type 2.