{"paper":{"title":"Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Cheryl E. Praeger, Joanna B. Fawcett","submitted_at":"2016-02-16T05:28:14Z","abstract_excerpt":"For a subgroup $L$ of the symmetric group $S_\\ell$, we determine the minimal base size of $GL_d(q)\\wr L$ acting on $V_d(q)^\\ell$ as an imprimitive linear group. This is achieved by computing the number of orbits of $GL_d(q)$ on spanning $m$-tuples, which turns out to be the number of $d$-dimensional subspaces of $V_m(q)$. We then use these results to prove that for certain families of subgroups $L$, the affine groups whose stabilisers are large subgroups of $GL_d(q)\\wr L$ satisfy a conjecture of Pyber concerning bases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04913","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"}