On the normalizers of some classes of subgroups in braid groups.
type: Item
instance of: scholarly article
title: On the normalizers of some classes of subgroups in braid groups.
zbMATH Open document ID: 1078.20037
DOI: 10.1023/A:1025006813982
published in: Mathematical Notes
publication date: 2004-12-02T00:00:00Z
review text: The authors describe the normalizers of some classes of subgroups in braid groups. In particular, they consider the subgroup \(\Pi=\langle\sigma^4_1,\sigma^4_2\rangle\times\langle\sigma_4\sigma_3 \sigma_2\sigma^2_1\sigma_2\sigma_3\sigma_4\rangle\subset R_5\) (\(R_5\) denotes the subgroup of colored 5-braids). It is known that \(\Pi\) is the direct product of free groups of rank 2. The authors find the normalizer \(N_{R_5}(\Pi)\) in \(R_5\). They also show that if \(H=H_1\times H_2\) is a finitely generated subgroup of \(\Pi\), \(H_1\) and \(H_2\) are not cyclic, then \(N_{K_5}(H)\subset N_{R_5}(\Pi)\).
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 2121008
zbMATH Keywords: braid groups
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: normalizers
zbMATH Keywords: finitely generated subgroups
author: V. N. Bezverkhniĭ
author: I. V. Dobrynina
reviewed by: Andrei M. Akimenkov
MaRDI profile type: Publication
full work available at URL: a:1025006813982
OpenAlex ID: W24286919
description: scientific article; zbMATH DE number 2121008