eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-12-30 3 6 160 164 10.12691/tjant-3-6-4 TJANT2015364 article Joris N. Buloron 1 Roberto B. Corcino rcorcino@yahoo.com 1 Lorna S. Almocera 2 Michael P. Baldado Jr. 3 Mathematics Department, Cebu Normal University, Cebu City, Philippines 6000 Science Cluster, University of the Philippines - Cebu Mathematics Department, Negros Oriental State University 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. http://pubs.sciepub.com/tjant/3/6/4/tjant-3-6-4.pdf sets non-involutions morphism