Commutator subgroups of twin groups and Grothendieck's cartographical groups

JOURNAL OF ALGEBRA

卷:530

Article

Dey, Soumya¹  Gongopadhyay, Krishnendu¹ 

[1] Indian Inst Sci Educ & Res IISER Mohali, Sect 81,PO Manauli, Mohali 140306, Punjab, India

关键词: Doodle;    Twin group;    Cartographical group;    Combinatorial maps;    Commutator subgroup;   

DOI  :  10.1016/j.jalgebra.2019.04.006

来源: Elsevier

【 摘 要 】

Let TWn be the twin group on n arcs, n >= 2, which is a right-angled Coxeter group. The group TWm+2 is isomorphic to Grothendieck's m-dimensional cartographical group C-m, m >= 1. In this paper we give a finite presentation for the commutator subgroup TWm+2', and prove that TWm+2' has rank 2m - 1. We derive that TWm+2' is free if and only if m <= 3. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free