A Jónsson group is a group where every proper subgroup is smaller than the group itself. Researchers have shown that there are Jónsson groups of infinite size if and only if there are Jónsson algebras of the same size. This means that the question of which sizes can have Jónsson groups is the same as the question of which sizes cannot. As a result, there are Jónsson groups of all different sizes. Additionally, a conjecture related to these groups has been proven true.