{"paper":{"title":"Minimality of the Semidirect Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Luie Polev, Menachem Shlossberg, Michael Megrelishvili","submitted_at":"2015-11-22T15:12:03Z","abstract_excerpt":"A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $G\\leftthreetimes P,$ where $G$ is a compact topological group and $P$ is a topological subgroup of $Aut(G)$. We prove that $G\\leftthreetimes P$ is minimal for every closed subgroup $P$ of $Aut(G)$. In case $G$ is abelian, the same is true for every subgroup $P \\subseteq Aut(G)$. We show, in contrast, that there exist a compact two-step nilpotent group $G$ and a subgroup $P$ of $Aut(G)$ such that $G\\leftthr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07021","kind":"arxiv","version":3},"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"}