{"paper":{"title":"Ideals in $\\mathcal{P} _G$ and $\\beta G$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Igor Protasov, Ksenia Protasova","submitted_at":"2017-04-08T13:46:09Z","abstract_excerpt":"For a discrete group $G$, we use the natural correspondence between ideals in the Boolean algebra $ \\mathcal{P}_G$ of subsets of $G$ and closed subsets in the Stone-$\\check{C}$ech compactifi-cation $\\beta G$ as a right topological semigroup to introduce and characterize some new ideals in $\\beta G$. We show that if a group $G$ is either countable or Abelian then there are no closed ideals in $\\beta G$ maximal in $G^*$, $G^* = \\beta G \\setminus G$, but this statement does not hold for the group $S_\\kappa$ of all permutations of an infinite cardinal $\\kappa$. We characterize the minimal closed i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02494","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"}