             Now let us suppose that we are given a group \(G\) of automorphisms of \(A\). Let us say that an automorphism \(\pi\); of \(A\) fixes an element \(x\) of \(V(A)\) if \(\pi(x) = x\). Clearly, if \(\pi \in G\) fixes every element of \(A\), it also fixes every element of \(V(A)\). Now it may be the case that, for certain elements \(x \in V(A)\), the fixing of the elements of a subset of \(A\) by any \(\pi\in G\) suffices to fix \(x\). We are therefore led to define a support for \(x\) to be a subset \(X\) of \(A\) such that, whenever \(\pi\in G\) fixes each member of \(X\), it also fixes \(x\). Members of \(V(A)\) possessing a finite support are called symmetric.