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http://dx.doi.org/10.14403/jcms.2020.33.1.113

FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS WITH HOMOTOPICALLY TRIVIAL TRANSLATIONS  

Koo, Daehwan (Daejeon Science High School for the Gifted)
Park, Eunmi (Daejeon Foreign Language High School)
Shin, Joonkook (Department of Mathematics Education Chungnam National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.33, no.1, 2020 , pp. 113-132 More about this Journal
Abstract
We show that if a finite group G acts freely with homotopically trivial translations on a 3-dimensional nilmanifold 𝓝p with the first homology ℤ2 ⊕ ℤp, then either G is cyclic or there exist finite nonabelian groups acting freely on 𝓝p which yield orbit manifolds homeomorphic to 𝓝/𝜋3 or 𝓝/𝜋4.
Keywords
affine conjugacy; almost Bieberbach group; group action; Heisenberg group; homotopically trivial translation;
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Times Cited By KSCI : 3  (Citation Analysis)
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