Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group (Q2401537)

In this paper, the authors study some subgroups of the automorphism group of the free group \(F_{n}\) with \(n\) generators (\(n \geq 2\)), in particular, \(\mathrm{IA}\)-automorphisms (it is remarkable that \(\mathrm{IA}(F_{2}) \simeq \mathrm{Inn}(F_{2}) \simeq F_{2}\) but \(\mathrm{IA}(F_{3})\) is not finitely presented), the basis-conjugating automorphism group \(\mathrm{Cb}_{n}\), the normal automorphisms \(\mathrm{Aut}_{N}(F_{n})\) and some others. The article is focused on their factorizations into a semidirect product on their automorphism groups and on their adjoint Lie algebras.