## Abstract

A stabilizer is a part of an algebra acting on a set. Specifically, let *X* be any algebra operating on a set *X* and let *A* be a subset of *X*. The stabilizer of *A*, sometimes denoted *St*(*A*), is the set of elements *a* of *A* for which \(a(S)\subseteq S\). The strict stabilizer is the set of \(a\in A\) for which \(a(A) = A\). In the other words, the stabilizer of *A* is the transporter of *A* to itself. The concept of stabilizers is introduced in Hilbert algebras by I. Chajda and R. Hala\(\check{s}\) (Mult. Valued Logic 8:139–148, 2002), [37]. In this paper, the authors studied the properties of stabilizers and relative stabilizers of a given subset of a Hilbert algebra . They proved that every stabilizer of a deductive system *C* of \(\mathcal {H}\) is also a deductive system which is a pseudo-complement of *C* in the lattice of all deductive systems of \(\mathcal {H}\). In (Borumand et al., in Sci. Bull. Ser. A 74(2):65–74, 2012), [15], A. Borumand Saeid and N. Mohtashamnia constructed quotient of residuated lattices via stabilizer and studied its properties. L. Torkzadeh (Math Sci 3(2):111–132, 2009), [232] introduced dual right and dual left stabilizers in bounded BCK-algebras and investigated the relationship between of them.