# Join of abelian subgroups of maximum order is intermediately characteristic

From Groupprops

Template:Sdf property satisfaction

## Statement

Let be a group of prime power order. Let denote the join of abelian subgroups of maximum order in , i.e., is the subgroup generated by all abelian subgroups of maximum order in . Then, is an intermediately characteristic subgroup of : for any subgroup of containing , is characteristic in .

In fact, is the join of abelian subgroups of maximum order in .