DECOMPOSABLE BRAIDS AS SUBGROUPS

The group of all decomposable 3-braids is the commutator subgroup of the group I3 of all 3-braids which leave strand positions invariant. The group of all 2-decomposable 4-braids is the commutator subgroup of I4, and the group of all decomposable 4-braids is explicitly characterized as a subgroup of the second commutator subgroup of 14.