In this paper, we investigate the structure of the automorphism groups of pure braid groups.
We prove that, for n> 3 n> 3, Aut (P_n) Aut (P n) is generated by the subgroup Aut _c (P_n)
Aut c (P n) of central automorphisms of P_n P n, the subgroup Aut (B_n) Aut (B n) of
restrictions of automorphisms of B_n B n on P_n P n and one extra automorphism w_n wn.
We also investigate the lifting and extension problem for automorphisms of some well-
known exact sequences arising from braid groups, and prove that that answers are negative …

In this paper, we investigate the structure of the automorphism groups of pure braid groups.
We prove that, for 𝑛> 3, Aut (𝑃𝑛) is generated by the subgroup Aut𝑐 (𝑃𝑛) of central
automorphisms of 𝑃𝑛, the subgroup Aut (𝐵𝑛) of restrictions of automorphisms of 𝐵𝑛 on 𝑃𝑛
and one extra automorphism 𝑤𝑛. We also investigate the lifting and extension problem for
automorphisms of some well-known exact sequences arising from braid groups, and prove
that that answers are negative in most cases. Specifically, we prove that no non-trivial …