# B-subgroup

This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup

View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions

## 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 is denoted as .

## Facts

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