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Let M be a 3-manifold obtained by performing a Dehn surgery on a knot in a solid torus. In the present paper we study when M contains a separating essential annulus. It is shown that M does not contain such an annulus in the majority of cases. As a corollary, we prove that symmetric knots in the 3-sphere which are not periodic knots of period 2 satisfy the cabling conjecture. This is an im- provement of a result of Luft and Zhang. We have one more application to a problem on Dehn surgeries on knots producing a Seifert bred manifold over the 2-sphere with exactly three ex- ceptional bres.

Dehn surgery on knots in solid tori creating essential annuli