Decomposable braids as subgroups of braid groups

H. Levinson
1975 Transactions of the American Mathematical Society  
Trie group of all decomposable 3-braids is trie commutator subgroup of the group /3 of all 3-braids which leave strand positions invariant. The group of all 2-decomposable 4-braids is the commutator subgroup of 74, and the group of all decomposable 4-braids is explicitly characterized as a subgroup of the second commutator subgroup of 74.
doi:10.1090/s0002-9947-1975-0362287-3 fatcat:rrzk6comcbcklispyxkblfuxma