  We introduce a linearly ordered lattice $\mu(Grp)$ of torsion theories in
simplicial groups. The torsion theories are defined where the
torsion/torsion-free subcategories are given by the simplicial groups with
bounded above/below Moore complex, respectively. These torsion theories extend
naturally the torsion theories in internal groupoids in groups. Connections of
this lattice with the homotopy groups are established since the homotopy groups
of a simplicial group can be calculated as the quotients of torsion subojects.
