{"paper":{"title":"On the group of automorphisms of the Brandt $\\lambda^0$-extension of a monoid with zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Oleg Gutik","submitted_at":"2016-09-20T10:29:11Z","abstract_excerpt":"The group of automorphisms of the Brandt $\\lambda^0$-extension $B^0_\\lambda(S)$ of an arbitrary monoid $S$ with zero is described. In particular we show that the group of automorphisms $\\mathbf{Aut}(B_{\\lambda}^0(S))$ of $B_{\\lambda}^0(S)$ is isomorphic to a homomorphic image of the group defines on the Cartesian product $\\mathscr{S}_{\\lambda}\\times \\mathbf{Aut}(S)\\times H_1^{\\lambda}$ with the following binary operation: \\begin{equation*}\n  [\\varphi,h,u]\\cdot[\\varphi^{\\prime},h^{\\prime},u^{\\prime}]= [\\varphi\\varphi^{\\prime},hh^{\\prime},\\varphi u^{\\prime}\\cdot uh^{\\prime}], \\end{equation*} whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06085","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"}