{"paper":{"title":"Large normal subgroup growth and large characteristic subgroup growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jan-Christoph Schlage-Puchta, Yiftach Barnea","submitted_at":"2017-03-22T21:39:20Z","abstract_excerpt":"The maximal normal subgroup growth type of a finitely generated group is $n^{\\log n}$. Very little is known about groups with this type of growth. In particular, the following is a long standing problem: Let $\\Gamma$ be a group and $\\Delta$ a subgroup of finite index. Suppose $\\Delta$ has normal subgroup growth of type $n^{\\log n}$, does $\\Gamma$ has normal subgroup growth of type $n^{\\log n}$? We give a positive answer in some cases, generalizing a result of M\\\"uller and the second author and a result of Gerdau. For instance, suppose $G$ is a profinite group and $H$ an open subgroup of $G$. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07866","kind":"arxiv","version":2},"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"}