In mathematics, in the area of abstract algebra known as group theory, a verbal subgroup is a subgroup of a group that is generated by all elements that can be formed by substituting group elements for variables in a given set of words.
On the other hand, the verbal subgroup for the set of words
is generated by the set of squares and their conjugates.
Verbal subgroups are the only fully characteristic subgroups of a free group and therefore represent the generic example of fully characteristic subgroups, (Magnus, Karrass & Solitar 2004, p. 75).
This group theory-related article is a stub.