TY - JOUR
T1 - Automorphisms of pure braid groups
AU - Bardakov, Valeriy G.
AU - Neshchadim, Mikhail V.
AU - Singh, Mahender
PY - 2018/9/1
Y1 - 2018/9/1
N2 - In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for n> 3 , Aut (P
n ) is generated by the subgroup Aut
c (P
n ) of central automorphisms of P
n , the subgroup Aut (B
n ) of restrictions of automorphisms of B
n on P
n and one extra automorphism w
n . 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 central automorphism of P
n can be extended to an automorphism of B
n .
AB - In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for n> 3 , Aut (P
n ) is generated by the subgroup Aut
c (P
n ) of central automorphisms of P
n , the subgroup Aut (B
n ) of restrictions of automorphisms of B
n on P
n and one extra automorphism w
n . 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 central automorphism of P
n can be extended to an automorphism of B
n .
KW - Braid group
KW - Central automorphism
KW - Extended mapping class group
KW - Pure braid group
KW - GROUP EXTENSIONS
UR - http://www.scopus.com/inward/record.url?scp=85020546801&partnerID=8YFLogxK
U2 - 10.1007/s00605-017-1073-7
DO - 10.1007/s00605-017-1073-7
M3 - Article
AN - SCOPUS:85020546801
VL - 187
SP - 1
EP - 19
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
SN - 0026-9255
IS - 1
ER -