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Word distance on the discrete Heisenberg group

Sébastien Blachère (2003)

Colloquium Mathematicae

We establish an exact formula for the word distance on the discrete Heisenberg group ℍ₃ with its standard set of generators. This formula is then used to prove the almost connectedness of the spheres for this distance.

W-perfect groups

Selami Ercan (2015)

Open Mathematics

In the present article we define W-paths of elements in a W-perfect group as a useful tools and obtain their basic properties.

σ -interpolation lattice-ordered groups

Michael R. Darnel (2000)

Czechoslovak Mathematical Journal

In [1], Jakubík showed that the class of σ -interpolation lattice-ordered groups forms a radical class, but left open the question of whether the class forms a torsion class. In this paper, we show that this class does indeed form a torsion class.

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