{"paper":{"title":"Growth behaviors in the range $e^{r^\\alpha}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"J\\'er\\'emie Brieussel","submitted_at":"2011-07-08T13:47:03Z","abstract_excerpt":"For every $\\alpha \\leq \\beta$ in a left neighborhood $[\\alpha_0,1]$ of 1, a group $G(\\alpha,\\beta)$ is constructed, the growth function of which satisfies $\\limsup \\frac{\\log \\log b_{G(\\alpha,\\beta)}(r)}{\\log r}=\\alpha$ and $\\liminf \\frac{\\log \\log b_{G(\\alpha,\\beta)}(r)}{\\log r}=\\beta$. When $\\alpha=\\beta$, this provides an explicit uncountable collection of groups with growth functions strictly comparable. On the other hand, oscillation in the case $\\alpha < \\beta$ explains the existence of groups with non comparable growth functions. Some period exponents associated to the frequency of osci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1632","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"}