• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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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 $C_4/C_2=C_2$).

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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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.

• Bulletin of the Korean Chemical Society
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• v.17 no.1
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• pp.46-50
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• 1996

Monoanionic nickel(Ⅲ) complexes, [Ni(dmbit)2]1- and [Ni(dmbbip)2]1- where dmbit2- and dmbbip2- denote 2-thiobenzo[d]-1,3-dithiole-5,6-dithiolate and 1,2-bis(isopropylthio)benzen-4,5-dithiolate, respectively, have been synthesized by the iodine oxidation of dianionic complexes. In the scanning electron microscopic(SEM) images, these complexes show the well-grown two-dimensional layered structures which are clearly comparable to the dianionic ones with three-dimensional structures. Magnetic susceptibilities of nickel(Ⅲ)complexes are fitted well with the two-dimensional Heisenberg antiferromagnet model of S=1/2 system resulting in the spin-exchange parameters (|J|/k) of 11.4 K and 0.45 K, respectively. The weaker magnetic interaction in [Ni(dmbbip)2]1- is resulted from the bulky isopropyl groups on the periphery of dmbbip ligand. EPR measurements for [Ni(dmbit)2]1- give the signal with axial symmetry and the anisotropic g-values for low-spin nickel(Ⅲ) (g//=2.158, g =2.030,gav=2.074 at 300 K; g//=2.162, g =2.038, gav=2.080 at 77 K). It is therefore concluded that nickel(Ⅱ) is oxidized to nickel(Ⅲ), rather than dmbit2- and dmbbip2- ligands are, by the iodine oxidation. The paramagnetic Ni(Ⅲ) would be located in the axial symmetry(D4h) with the electronic configuration of (dxz2dyz2dz22dxy1dx2-y20).