Palindromic automorphisms of free groups

JOURNAL OF ALGEBRA

卷:438

Article

Bardakov, Valeriy G.^1,2,3  Gongopadhyay, Krishnendu⁴  Singh, Mahender⁴ 

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Chelyabinsk State Univ, Lab Quantum Topol, Chelyabinsk 454001, Russia

[4] Indian Inst Sci Educ & Res, Manauli 140306, Punjab, India

关键词: Free group;    Palindromic automorphism;    Representation;    Residual nilpotence;    Torelli group;   

DOI  :  10.1016/j.jalgebra.2015.05.014

来源: Elsevier

【 摘 要 】

Let F-n be the free group of rank n with free basis X = {x(1),..., x(n)}. A palindrome is a word in X-+/- 1 that reads the same backwards as forwards. The palindromic automorphism group Pi A(n) of F-n consists of those automorphisms that map each x(i) to a palindrome. In this paper, we investigate linear representations of Pi A(n), and prove that Pi A(2) is linear. We obtain conjugacy classes of involutions in Pi A(2), and investigate residual nilpotency of Pi A(n) and some of its subgroups. Let IA(n) be the group of those automorphisms of F-n that act trivially on the abelianisation, PIn be the palindromic Torelli group of F-n, and let E Pi A(n) be the elementary palindromic automorphism group of F-n. We prove that PIn = IA(n) = IA(n) boolean AND E Pi A'(n). This result strengthens a recent result of Fullarton [2]. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free