A presentation for the stabilizer of an element in a free product (Q1086353)

The authors consider the free product of finitely many (freely) indecomposable groups none of which is infinite cyclic. They impose certain natural assumptions on the factors and prove that under these assumptions the stabilizer in Aut G of an element of G is finitely presented. The natural assumptions are, for example, that each factor is finitely presented, the automorphism group of each factor is finitely presented, the stabilizer of a subset of a factor in the corresponding automorphism group is finitely presented. This can be considered as a generalization (modulo the exclusion of infinite cyclic factors) of a corresponding result of \textit{J. McCool} [J. Algebra 35, 205-213 (1975; Zbl 0325.20025)] for the stabilizer of an element of a free group. The techniques used for the proofs, too technical to be explained here, are based on those developed by the authors [in their papers Math. Z. 185, 487-504 (1984; Zbl 0537.20010)] and 186, 335-361 (1984; Zbl 0542.20012)].