{"paper":{"title":"Automorphisms of dihedral-like automorphic loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mouna Aboras, Petr Vojt\\v{e}chovsk\\'y","submitted_at":"2017-12-18T16:51:28Z","abstract_excerpt":"Automorphic loops are loops in which all inner mappings are automorphisms. A large class of automorphic loops is obtained as follows: Let $m$ be a positive even integer, $G$ an abelian group, and $\\alpha$ an automorphism of $G$ that satisfies $\\alpha^2=1$ if $m>2$. Then the dihedral-like automorphic loop $\\mathrm{Dih}(m,G,\\alpha)$ is defined on $\\mathbb Z_m\\times G$ by $(i,u)(j,v)=(i+j, ((-1)^{j}u+v)\\alpha^{ij})$. We prove that two finite dihedral-like automorphic loops $\\mathrm{Dih}(m,G,\\alpha)$, $\\mathrm{Dih}(\\overline{m},\\overline{G},\\overline{\\alpha})$ are isomorphic if and only if $m=\\ove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06516","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":""},"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"}