Wielandt series and defects of subnormal subgroups in finite soluble groups
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.
In the present article we define W-paths of elements in a W-perfect group as a useful tools and obtain their basic properties.
In [1], Jakubík showed that the class of -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.