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

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.

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