Maximal nilpotent quotients of 3-manifold groups

DOI10.4310/MRL.1997.V4.N2.A9zbMath0891.57022arXivmath/9612216MaRDI QIDQ1364795

Peter Teichner

Publication date: 28 August 1997

Published in: Mathematical Research Letters (Search for Journal in Brave)

Abstract: We show that if the lower central series of the fundamental group of a closed oriented $3$-manifold stabilizes then the maximal nilpotent quotient is a cyclic group, a quaternion $2$-group cross an odd order cyclic group, or a Heisenberg group. These groups are well known to be precisely the nilpotent fundamental groups of closed oriented $3$-manifolds.

Full work available at URL: https://arxiv.org/abs/math/9612216

zbMATH Keywords

fundamental groups of 3-manifoldsmaximal nilpotent quotient

Mathematics Subject Classification ID

Finite nilpotent groups, (p)-groups (20D15)

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