{"paper":{"title":"Local Conjugacy in $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.GR","authors_text":"H. Kim","submitted_at":"2017-05-30T14:34:20Z","abstract_excerpt":"Subgroups $H_1$ and $H_2$ of a group $G$ are said to be locally conjugate if there is a bijection $f: H_1 \\rightarrow H_2$ such that $h$ and $f(h)$ are conjugate in $G$ for every $h \\in H_1$. This paper studies local conjugacy among subgroups of $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$, where $p$ is an odd prime, building on Sutherland's categorizations of subgroups of $\\text{GL}_2(\\mathbb{Z}/p\\mathbb{Z})$ and local conjugacy among them. There are two conditions that locally conjugate subgroups $H_1$ and $H_2$ of $\\text{GL}_2(\\mathbb{Z}/p^2\\mathbb{Z})$ must satisfy: letting $\\varphi: \\text{GL}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00075","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"}