Join of all abelian normal subgroups

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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


Suppose G is a group. The join of all abelian normal subgroups of G is the subgroup of G defined as the join of all the abelian normal subgroups of G.

If G is a finite group (or more generally a group satisfying ascending chain condition on normal subgroups) then this is equivalent to the join of all subgroups that are maximal among abelian normal subgroups.