• 충청수학회지
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• 제32권3호
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• pp.365-381
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• 2019

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_2$, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in ${\pi}_1$, two in ${\pi}_2$ or ${\pi}_{5,i}$(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

• 대한수학회지
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• 제43권5호
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• pp.1115-1128
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• 2006

Let $so(3)\tilde{\times}R^3$ be the 6-dimensional nilpotent Lie group with group operation (s, x)(t, y) = $(s+t+xy^t-yx^t,\;x+y)$. We prove that the maximal order of the holonomy groups of all infra-nilmanifolds with $so(3)\tilde{\times}R^3$-geometry is 16.

• 충청수학회지
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• 제31권4호
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• pp.475-486
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• 2018

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\bigoplus}{\mathbb{Z}}_2$ which yield an orbit manifold reversing fiber orientation, up to topological conjugacy. We show that those nonabelian groups are $D_4$(the dihedral group), $Q_8$(the quaternion group), and $C_8.C_4$(the $1^{st}$ non-split extension by $C_8$ of $C_4$ acting via $C_4/C_2=C_2$).

• 충청수학회지
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• 제33권1호
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• pp.113-132
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• 2020

We show that if a finite group G acts freely with homotopically trivial translations on a 3-dimensional nilmanifold 𝓝_p with the first homology ℤ² ⊕ ℤ_p, then either G is cyclic or there exist finite nonabelian groups acting freely on 𝓝_p which yield orbit manifolds homeomorphic to 𝓝/𝜋₃ or 𝓝/𝜋₄.