{"paper":{"title":"Choosing elements from finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael Vaughan-Lee","submitted_at":"2017-07-30T17:53:40Z","abstract_excerpt":"In two important papers from 1960 Graham Higman introduced the notion of PORC functions, and he proved that for any given positive integer $n$ the number of $p$-class two groups of order $p^n$ is a PORC function of $p$. A key result in his proof of this theorem is the following: \"The number of ways of choosing a finite number of elements from the finite field of order $q^n$ subject to a finite number of monomial equations and inequalities between them and their conjugates over GF($q$), considered as a function of $q$, is PORC.\" Higman's proof of this result involves five pages of homological a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09652","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"}