{"paper":{"title":"Substitution groups of formal power series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Agust\\'in D'Alessandro, Fernando Szechtman","submitted_at":"2026-06-09T21:31:04Z","abstract_excerpt":"Let $G$ be the group of power series $x+a_2x^2+a_3x^3+\\cdots\\in R[[x]]$ under substitution, where $R$ is a commutative ring with $1\\neq 0$ of prime characteristic $p$. Given any $n\\geq 1$, the subgroup $K_n=\\{x+a_{n+1}x^{n+1}+a_{n+2}x^{n+2}+\\cdots\\,|\\, a_i\\in R\\}$ is normal in $G$, and the quotient $G_n=G/K_n$ is the group of truncated polynomials over $R$ of degree $\\leq n$ under substitution. In this paper, we compute the exponent of the image of $K_r$ in $G_n$, for all $r,n\\geq 1$, indicating in every case a family of elements realizing this exponent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11461","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11461/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}