# NONABELIAN GROUP ACTIONS ON 3-DIMENSIONAL NILMANIFOLDS WITH THE FIRST HOMOLOGY ℤ2⊕ℤ2

• Han, Mina (Cheonan Wolbong Middle School) ;
• Koo, Daehwan (Daejeon Science High School for the Gifted) ;
• Shin, Joonkook (Department of Mathematics Education Chungnam National University)
• Accepted : 2019.08.14
• Published : 2019.08.15

#### Abstract

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.

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