Is this a reduction from decision problem to non-decision problem?
It seems that the author uses the notation $A\le_p B$, where $A,B$ can be either function or decision problems, for saying that given an oracle for $B$, one can solve $A$ in polynomial time.

It is then shown that the isomorphism problem is reducible to finding the generators of a setwise stabilizer group (STAB) by showing that it is reducible to finding the generators of the automorphism group (AUT), and that $AUT\le_p STAB$. The latter is shown by viewing vertex permutations as an operation over vertex pairs, and seeking the generators of the corresponding stabilizing group relative to $E$.