Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 3 6 2015 12 30 ?sets and Structure-Preserving Maps 160 164 EN Joris N. Buloron Roberto B. Corcino Mathematics Department, Cebu Normal University, Cebu City, Philippines 6000 Lorna S. Almocera Michael P. Baldado Jr. TJANT2015364 10.12691/tjant-3-6-4 2015 9 4 2015 10 12 2015 12 28 This paper investigates ?sets of groups in relation to structure-preserving maps. It shows connections between non-involutions of groups and the concept of ?sets. In particular, we prove that the existence of a semigroup isomorphism between the families of ?sets of two groups is equivalent to an existence of a special type of bijection between the subsets containing all elements of orders greater than two of the groups.