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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


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).


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