• 대한수학회지
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• 제54권5호
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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.

• 대한수학회지
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• 제42권4호
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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.

• 충청수학회지
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• 제10권1호
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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.

• 충청수학회지
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• 제13권2호
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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.

• 대한수학회지
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• 제56권1호
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• pp.285-287
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• 2019

• 충청수학회지
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• 제14권2호
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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.

• 충청수학회지
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• 제19권4호
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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.].

• 충청수학회지
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• 제20권3호
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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].

• 충청수학회지
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• 제18권2호
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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.

• 충청수학회지
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• 제16권1호
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• pp.123-135
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• 2003

We shall study the automorphism group of the quaternionic Heisenberg group $\mathcal{H}_7(\mathbb{H})=\mathbb{R}^3{\tilde{\times}}\mathbb{H}$ which is important to investigate an almost Bieberbach group of a 7-dimensinal infra-nilmanifold and show that Aut$$(\mathbb{R}^3{\tilde{\times}}\mathbb{R}^4){\sim_=}Hom(\mathbb{R}^4,\mathbb{R}^3){\rtimes}O(J;2,2)$$.