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arXiv · 2411.15547

On the $z$-classes of Palindromic automorphisms of Free Groups

Krishnendu Gongopadhyay·Lokenath Kundu·Shashank Vikram Singh
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Abstract

The palindromic automorphism group is a subgroup of the automorphism group $Aut(F_3).$ We establish a necessary and sufficient condition for a matrix in $GL_n(\mathbb{Z})$ representing a palindromic automorphism of $F_n.$ We prove that the number of the $z$-classes in $\Pi A(F_n)$ is infinite. We further classify the conjugacy classes of the reducible palindromic automorphisms.

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Krishnendu Gongopadhyay, Lokenath Kundu, Shashank Vikram Singh. 2024-11-23. On the $z$-classes of Palindromic automorphisms of Free Groups. https://arxiv.org/abs/2411.15547

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