The outer automorphism groups of two-generator, one-relator groups with torsion (Q2816994)

One relator groups with torsion play a fundamental and motivating class of non-free finitely presented groups, and in particular the two-generator, one-relator groups with torsion because each one-relator group with torsion is embeddable into a two-generator one, and each two-generator subgroup of a one-relator group with torsion in either a free product of two cyclic groups or a two-generator, one-relator group with torsion. Also, if a two-generator, one-relator group with torsion is not decomposable as a free product of two cyclic groups, then it has only one Nielsen equivalence class of generating pairs, and in this case therefore its outer automorphism group is a quotient of a subgroup of the outer automorphism group of the free group of rank two.NEWLINENEWLINE This is the background for the complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion given in this interesting paper. The proofs are finally based on a geometric algorithm given by \textit{F. Dahmani} and \textit{V. Guirardel} [Geom. Funct. Anal. 21, No. 2, 223--300 (2011; Zbl 1258.20034)].