B-subgroup

Definition
The B-subgroup of a group is defined as the product of those 2-components of the group that are not contained in the layer (which is the commuting product of the components). Th B-subgroup of a group $$G$$ is denoted as $$B(G)$$.

Facts
For a core-free group, the B-subgroup is trivial, since the 2-layer equals the layer.