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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.
Received: 27.02.2014
Citation:
A. I. Nekritsuhin, “On some properties palindromes of automorphisms of a free group”, Chebyshevskii Sb., 15:1 (2014), 141–145
Linking options:
https://www.mathnet.ru/eng/cheb332 https://www.mathnet.ru/eng/cheb/v15/i1/p141
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Abstract page: | 183 | Full-text PDF : | 83 | References: | 45 |
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