{"paper":{"title":"Palindromic Automorphisms of Free Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Krishnendu Gongopadhyay, Mahender Singh, Valeriy G. Bardakov","submitted_at":"2014-11-02T10:45:02Z","abstract_excerpt":"Let $F_n$ be the free group of rank $n$ with free basis $X=\\{x_1,\\dots,x_n \\}$. A palindrome is a word in $X^{\\pm 1}$ that reads the same backwards as forwards. The palindromic automorphism group $\\Pi A_n$ of $F_n$ consists of those automorphisms that map each $x_i$ to a palindrome. In this paper, we investigate linear representations of $\\Pi A_n$, and prove that $\\Pi A_2$ is linear. We obtain conjugacy classes of involutions in $\\Pi A_2$, and investigate residual nilpotency of $\\Pi A_n$ and some of its subgroups. Let $IA_n$ be the group of those automorphisms of $F_n$ that act trivially on th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0240","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}