Bordered surfaces in the 3-sphere with maximum symmetry

In the present paper we obtain analogous results for the case of bordered surfaces Σ (i.e. with non-empty boundary, orientable or not). Now the genus g gets replaced by the algebraic genus α of Σ (the rank of its free fundamental group); for each α>1 we determine the maximum order mα of an action of G, classify the topological types of the corresponding surfaces (topological genus, number of boundary components, orientability) and their embeddings into S3. For example, the maximal possibility 12(α−1) is obtained for the finitely many values α=2,3,4,5,9,11,25,97,121 and 241.