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We also show that for $p=2$ this claim is not true and the growth rate of $BS(1,2)$ is equal to the positive root of $x^3-x^2-2$, whilst the one of the lamplighter group $\\mathcal{L}_2$ is equal to the golden ratio $(1+\\sqrt5)/2$. The latter value also serves to show that the lower bound of A.Mann from [Mann, Journal of Algebra 326, no. 1 (2011) 208--217] for the growth rates of non-semidire"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.03569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-11T07:10:55Z","cross_cats_sorted":[],"title_canon_sha256":"1c1be5da143fdbd2336378fe7da7ad576c3d47542a68a861d711aec24c2dd1f3","abstract_canon_sha256":"0862b880113704f667ecf61152a98f6d08f189c85b69c0448cd5e3bbbee9c05f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:03.804736Z","signature_b64":"N8rKNRZWfbXsFEFFpkUZJi7Sc4CH3UkZ+xkMx7g3h1u/SY1Ymzi31hw1702LKsT62dm3BwoCZTXnPwhiJ25fCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a0b624f6fcdc820ca84a07661b022db0782f682bfef5b6e56ff6db9444f9ef2","last_reissued_at":"2026-05-18T01:53:03.804166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:03.804166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal exponential growth rates of metabelian Baumslag-Solitar groups and lamplighter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexey Talambutsa, Michelle Bucher","submitted_at":"2015-06-11T07:10:55Z","abstract_excerpt":"We prove that for any prime $p\\geq 3$ the minimal exponential growth rate of the Baumslag-Solitar group $BS(1,p)$ and the lamplighter group $\\mathcal{L}_p=(\\mathbb{Z}/p\\mathbb{Z})\\wr \\mathbb{Z}$ are equal. 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