REPRESENTATIONS OF THE FINITE GROUPS BY SYMMETRY GROUPS OF OPERATIONS
Jerzy Płonka · Demonstratio Mathematica · 1977
Let j §Q be the group of all permutations of the set K n = Let (Xjf (x.|,... ,xn)) be a universal algebra.We denote by S(f) the symmetry group of the operation f i.e.the group of all permutations f of the set K satysfying in CL the identity f(x1l...fxQ) = f (x^ 1 ^ ,... ) (see [2]).In this paper we show that if P is a subgroup of §n then there exists a finite algebra 01 =»(X;f(x.j,... ,xn)) without constants such that P = S(f).To show that, we prove a more general theorem (see section 1).