Allenby, R. B. J. T.; Kim, Goansu; Tang, C. Y. On the residual finiteness of \(\text{Out}(\pi_1(M))\) of certain Seifert manifolds. (English) Zbl 1040.20023 Algebra Colloq. 10, No. 2, 121-126 (2003). It is shown that the outer automorphism group \(\text{Out}(\pi_1(M))\) of the fundamental group of a 3-dimensional Seifert fiber space \(M\) with non-empty boundary is residually finite. The proof uses a result of E. K. Grossman stating that \(\text{Out}(G)\) is residually finite for a group \(G\) which is conjugacy separable and has the property that an automorphism of \(G\) which maps each element to a conjugate is an inner automorphism; see [J. Lond. Math. Soc., II. Ser. 9, 160-164 (1974; Zbl 0292.20032)], where it is also shown that the outer automorphism group and mapping class group of a compact orientable surface is residually finite. Reviewer: Bruno Zimmermann (Trieste) Cited in 5 Documents MSC: 20E26 Residual properties and generalizations; residually finite groups 20E36 Automorphisms of infinite groups 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 57M05 Fundamental group, presentations, free differential calculus 57M07 Topological methods in group theory Keywords:residual finiteness; outer automorphism groups of fundamental groups of Seifert fiber spaces Citations:Zbl 0292.20032 PDFBibTeX XMLCite \textit{R. B. J. T. Allenby} et al., Algebra Colloq. 10, No. 2, 121--126 (2003; Zbl 1040.20023)