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

Abstract

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology Z2 ⊕ Z2, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in π1, two in π2 or π5,i(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

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