Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Turkish Journal of Analysis and Number Theory. 2015, 3(6), 160-164
DOI: 10.12691/tjant-3-6-4
Open AccessArticle

−sets and Structure-Preserving Maps

Joris N. Buloron1, Roberto B. Corcino1, , Lorna S. Almocera2 and Michael P. Baldado Jr.3

1Mathematics Department, Cebu Normal University, Cebu City, Philippines 6000

2Science Cluster, University of the Philippines - Cebu

3Mathematics Department, Negros Oriental State University

Pub. Date: December 30, 2015

Cite this paper:
Joris N. Buloron, Roberto B. Corcino, Lorna S. Almocera and Michael P. Baldado Jr.. −sets and Structure-Preserving Maps. Turkish Journal of Analysis and Number Theory. 2015; 3(6):160-164. doi: 10.12691/tjant-3-6-4


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.

−sets non-involutions morphism

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/


[1]  J. N. Buloron and J. M. P. Balmaceda. Conjugation action on the family of minimum sets of a group. MS Thesis, University of the Philippines - Diliman, 2015.
[2]  T. Haynes, S. Hedetniemi and P. Slater. Fundamentals of domination in graphs (Marcel Dekker, Inc., New York, 1998).
[3]  T. W. Hungerford. Algebra (Springer-Verlag, Inc., New York, 1976).
[4]  V. Kandasamy and F. Smarandache. Groups as graphs (Editura CuArt, Romania, 2009).
[5]  D. C. Kurtz. Foundations of abstract mathematics (Singapore: McGraw-Hill Inc., 1992).
[6]  C. J. S. Rosero, J. M. Ontolan, J. N. Buloron and M. P. Baldado, Jr. On the −sets of finite groups. International Journal of Algebra. 8 (2014), 623-628.
[7]  C. J. S. Rosero, J. M. Ontolan, J. N. Buloron and M. P. Baldado, Jr. Some properties of −sets of a group. International Mathematical Forum. 9 (2014), 1035-1040.