ON SOME PROPERTIES PALINDROMES OF AUTOMORPHISMS OF A FREE GROUP
https://doi.org/10.22405/2226-8383-2014-15-1-141-145
Abstract
Let Fn, n > 2 denote the free group generated by n letters x1, . . . , . . . , xn and Aut(Fn) be the automorphism group of Fn. Certain subgroup of the group Aut(Fn) are considered. First of all examine the palindromic automorphism group ПA(Fn). This group first defined Collins in [1], which is related to congruence subgroups of SL(n,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 Fn. Second theme of this paper connect with faithfulness of a linear representation of the group elementary palindromic automorphisms EПA(Fn). It is show that some concrete representation are not linear. For this use the subgroup IA(Fn) of group Aut(Fn) [15].
About the Author
A. I. Nekritsuhin
Тульский государственный педагогический университет им. Л. Н. Толстого
Russian Federation
Russian Federation
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Review
For citations:
Nekritsuhin A.I. ON SOME PROPERTIES PALINDROMES OF AUTOMORPHISMS OF A FREE GROUP. Chebyshevskii Sbornik. 2014;15(1):141-145. (In Russ.) https://doi.org/10.22405/2226-8383-2014-15-1-141-145
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