On the $z$-classes of Palindromic automorphisms of Free Groups
Krishnendu Gongopadhyay, Lokenath Kundu, Shashank Vikram Singh

TL;DR
This paper investigates the structure of palindromic automorphisms of free groups, providing conditions for their matrix representations, proving the infinitude of their $z$-classes, and classifying conjugacy classes of reducible automorphisms.
Contribution
It establishes a necessary and sufficient condition for matrices representing palindromic automorphisms and classifies conjugacy classes, revealing the infinite nature of $z$-classes.
Findings
Number of $z$-classes in $$-classes is infinite.
Provides a matrix criterion for palindromic automorphisms.
Classifies conjugacy classes of reducible automorphisms.
Abstract
The palindromic automorphism group is a subgroup of the automorphism group We establish a necessary and sufficient condition for a matrix in representing a palindromic automorphism of We prove that the number of the -classes in is infinite. We further classify the conjugacy classes of the reducible palindromic automorphisms.
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · Japanese History and Culture
