Computing the decomposition group of a zero-dimensional ideal by elimination method

In this note, we show that the decomposition group Dec(I) of a zero-dimensional radical ideal I in K[x1, . . . , xn] can be represented as the direct sum of several symmetric groups of polynomials based upon using Gröbner bases. The new method makes a theoretical contribution to discuss the decomposition group of I by using Computer Algebra without considering the complexity. As one application, we also present an approach to yield new triangular sets in computing triangular decomposition of polynomial sets P if Dec(< P >) is known.