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Commutator subgroups of Hantzsche–Wendt groups
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Bartosz Putrycz
Published/Copyright:
June 18, 2007
Abstract
A generalized Hantzsche–Wendt (GHW) group is by definition the fundamental group of a flat n-manifold with holonomy group ℤ2n-1, and a Hantzsche–Wendt (HW) group is a GHW group corresponding to an orientable manifold (with n odd). We prove that for any n-dimensional HW group with n > 3, the commutator subgroup and translation subgroup are equal, and hence the abelianization of the group is ℤ2n-1. We also give examples of GHW groups with the same property for all n > 4. These groups are all examples of torsion-free metabelian groups with abelianizations ℤ2k for some k > 3.
Received: 2006-05-24
Published Online: 2007-06-18
Published in Print: 2007-05-23
© Walter de Gruyter
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Articles in the same Issue
- Transitivity properties for group actions on buildings
- Fields, values and character extensions in finite groups
- Primitive sharp permutation groups with large solvable subgroups
- On the size of the nilpotent residual in finite groups
- On the commuting complex of finite metanilpotent groups
- Soluble normally constrained pro-p-groups
- Comparing quasi-finitely axiomatizable and prime groups
- A finitely presented torsion-free simple group
- Andrews–Curtis groups and the Andrews–Curtis conjecture
- Residual finiteness of outer automorphism groups of certain tree products
- Commutator subgroups of Hantzsche–Wendt groups
