Join of all abelian normal subgroups
From Groupprops
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
Suppose is a group. The join of all abelian normal subgroups of
is the subgroup of
defined as the join of all the abelian normal subgroups of
.
If 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.