{"paper":{"title":"On large sequential groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alexander Shibakov","submitted_at":"2016-04-29T15:26:30Z","abstract_excerpt":"We construct, using $\\diamondsuit$, an example of a sequential group $G$ such that the only countable sequential subgroups of $G$ are closed and discrete, and the only quotients of $G$ that have a countable pseudocharacter are countable and Fr\\'echet. We also show how to construct such a $G$ with several additional properties (such as make $G^2$ sequential, and arrange for every sequential subgroup of $G$ to be closed and contain a nonmetrizable compact subspace, etc.).\n  Several results about $k_\\omega$ sequential groups are proved. In particular, we show that each such group is either locall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08874","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"}