On the $z$-classes of Palindromic automorphisms of Free Groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908639371984896 |
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| author | Gongopadhyay, Krishnendu Kundu, Lokenath Singh, Shashank Vikram |
| author_facet | Gongopadhyay, Krishnendu Kundu, Lokenath Singh, Shashank Vikram |
| contents | 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 $ΠA(F_n)$ is infinite. We further classify the conjugacy classes of the reducible palindromic automorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $z$-classes of Palindromic automorphisms of Free Groups Gongopadhyay, Krishnendu Kundu, Lokenath Singh, Shashank Vikram Group Theory 20F28 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 $ΠA(F_n)$ is infinite. We further classify the conjugacy classes of the reducible palindromic automorphisms. |
| title | On the $z$-classes of Palindromic automorphisms of Free Groups |
| topic | Group Theory 20F28 |
| url | https://arxiv.org/abs/2411.15547 |