We show that every countable group Q is isomorphic to Out(N) where N is a finitely generated subgroup of a countable C′(1/6) small-cancellation group G. Furthermore, when Q is finitely presented, we can choose G to be finitely presented and residually finite.

Journal of Pure and Applied Algebra
School of Mathematics and Statistics

Bumagin, I, & Wise, D.T. (Daniel T.). (2005). Every group is an outer automorphism group of a finitely generated group. Journal of Pure and Applied Algebra, 200(1-2), 137–147. doi:10.1016/j.jpaa.2004.12.033