Systems of generators for normalizers of some elements of a braid group. (Russian) Zbl 0548.20022

Gurzo, G. G.

Izv. Akad. Nauk SSSR, Ser. Mat. 48, No. 3, 476-519 (1984).

The author determines the normalisers of the following elements in the braid group \(B_{n+1}: \sigma_{i,j}=\sigma_ i\sigma_{i+1}...\sigma_ j, \tau_{j,i}=\sigma_ j\sigma_{j- 1}...\sigma_ i, (\sigma_{i,j}\tau_{j,i})^ t\) and \((\tau_{j,i}\sigma_{i,j})^ t\) and \((\sigma_{i,j}\sigma_{i,j- 1}...\sigma_{i,i})^ t,\) where 1\(\leq i\leq j\leq n\) and t is a positive integer. The results are too complicated to give here.

Reviewer: S.Moran

MSC:

20F36	Braid groups; Artin groups
20E07	Subgroup theorems; subgroup growth
20F05	Generators, relations, and presentations of groups

Keywords:

normalisers; braid group