The derived subgroup is the subgroup generated by the set of all commutators of a group $G$.
I always used to forget that "generated by" part. Soon I will be teaching a group theory course and wish to prevent students from making the same mistake.
Is there an easy example, presentable to beginning group theory students, of a group in which the set of commutators is proper in the derived subgroup?
I am aware of this question, but the students I will be talking to will be below the level of wreath products, so the paper linked there isn't of any use. Is there perhaps an example in the infinite groups which would be easier to understand?