Dehn surgery on knots in solid tori creating essential annuli

Let be a -manifold obtained by performing a Dehn surgery on a knot in a solid torus. In the present paper we study when contains a separating essential annulus. It is shown that does not contain such an annulus in the majority of cases. As a corollary, we prove that symmetric knots in the -sphere which are not periodic knots of period satisfy the cabling conjecture. This is an improvement of a result of Luft and Zhang. We have one more application to a problem on Dehn surgeries on knots producing a Seifert fibred manifold over the -sphere with exactly three exceptional fibres.