{"paper":{"title":"On the Laxton Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Masanari Kida, Miho Aoki","submitted_at":"2018-09-21T08:08:42Z","abstract_excerpt":"We redefine a multiplicative group structure on the set of equivalence classes of rational sequences satisfying a fixed linear recurrence of degree two, which was defined by R. R. Laxton in his paper \"On groups of linear recurrences I\" published in Duke Math. 36, 721--736 (1969). In the article, he also defined some natural subgroups of the group, and determined the structures of their quotient groups. However, he did not study the whole group itself. Nothing has been known about the structure of Laxton's whole group and its interpretation. The aims of this paper are to redefine Laxton's group"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07973","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"}