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In this article, we develop the theory of SAGBI bases in <i>G</i>-algebras and create a criterion through which we can check if a set of polynomials in a <i>G</i>-algebra is a SAGBI basis or not. Moreover, we will construct an algorithm to compute SAGBI bases from a subset of polynomials contained in a subalgebra of a <i>G</i>-algebra.