On some properties palindromes of automorphisms of a free group

A. I. Nekritsuhin

Tula State Pedagogical University

Abstract: Let $F_n$, $n\ge2$ denote the free group generated by $n$ letters $x_1,\ldots,$ $\ldots,x_n$ and $Aut(F_n)$ be the automorphism group of $F_n$. Certain subgroup of the group $Aut(F_n)$ are considered.
First of all examine the palindromic automorphism group $\text{П}A(F_n)$. This group first defined Collins in [1], which is related to congruence subgroups of $SL(n,\mathbb Z)$, and symmetric automorphism group of the free group. It is calculate the center of the palindromic automorphism group. For this used combinatorics on words of the group $F_n$.
Second theme of this paper connect with faithfulness of a linear representation of the group elementary palindromic automorphisms $E\text{П}A(F_n)$. It is show that some concrete representation are not linear. For this use the subgroup $IA(F_n)$ of group $Aut(F_n)$ [15].

Keywords: free group, palindromes automorphism.

UDC: 519.4

Received: 27.02.2014