Variety of groups is congruence-permutable
This article gives the statement, and possibly proof, of a property satisfied by the variety of groups
View a complete list of such property satisfactions
Translation to the language of groups
The translation of this statement to the ordinary language of groups is: given two normal subgroups of a group, their product is a normal subgroup. In other words, any two normal subgroups permute and their product is also a normal subgroup.
Proof in terms of other results
The result can be thought of as a combination of two facts: