Auto-Engel Polygroups

Document Type : Original Scientific Paper


1 Department of Mathematics, Payame Noor, University, Tehran, Iran

2 School of Mathematics, Statistics and Computer Sciences, University of Tehran, Tehran, I. R. Iran



This paper introduces the concept of auto–Engel polygroups via the heart of hypergroups and investigates the relation between of auto–Engel polygroups and auto–nilpotent polygroups. Indeed, we show that the concept of heart of hypergroups plays an important role on construction of auto–Engel polygroups. This study considers the notation of characteristic set in hypergroups with respect to automorphism of hypergroups and shows that the heart of hypergroups is a characteristic set in hypergroups.


[1] R. Ameri and E. Mohammadzadeh, Engel groups derived from hypergroups, European J. Combin. 44 (2015) 191 − 197.
[2] R. Ameri, M. Hamidi and A. Mosayebi-Dorcheh, On auto-nilpotent polygroups, submitted.
[3] R. Ameri, M. Hamidi and A. Mosayebi-Dorcheh, On Engel polygroup-based graphs, submitted.
[4] J. Chvalina, S. Hoskova-Mayerova and A. D. Nezhad, General actions of hyperstructures and some applications, An. Ştiinţ. Univ. "Ovidius” Constanţa Ser. Mat. 21 (1) (2013) 59 − 82.
[5] H. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Boston, MA, 2002.
[6] H. Corsini, Prolegomena of Hypergroup Theory, 2nd ed., Aviani, Tricesimo UD, Italy, 1993.
[7] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, Int. Acad. Press, USA, 2007.
[8] M. Hamidi and A. R. Ashrafi, Fundamental relation and automorphism group of very thin Hv–groups, Comm. Algebra 45 (1) (2017) 130 − 140.
[9] M. Hamidi, A. Borumand Saeid and V. Leoreanu, Divisible groups derived
from divisible hypergroups, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 79 (2) (2017) 59 − 70.
[10] M. Hamidi and V. Leoreanu-Fotea, On (2-closed) regular hypergroup, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 80 (4) (2018) 173 − 186.
[11] F. Marty, Sur une généralisation de la notion de groupe, in: Huitiéme Congr. Math. Scan. Stockholm (1934) pp. 45 − 49.
[12] M. R. R. Moghaddam, H. Safa and A. K. Mousavi, Autocommutators and auto-Bell groups, Bull. Korean Math. Soc. 51 (4) (2014) 923 − 931.
[13] M. A. Rostamyari, A. K. Mousavi and M. R. R. Moghaddam, On auto-Engle groups and auto-Bell groups, Southeast Asian Bull. Math. 39 (2015) 265–272.
[14] T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Inc. Florida, 1994.