{"paper":{"title":"Wreath determinants for group-subgroup pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kazufumi Kimoto, Kazutoshi Tachibana, Kei Hamamoto, Masato Wakayama","submitted_at":"2014-06-10T05:31:10Z","abstract_excerpt":"The aim of the present paper is to generalize the notion of the group determinants for finite groups. For a finite group $G$ of order $kn$ and its subgroup $H$ of order $n$, one may define an $n$ by $kn$ matrix $X=(x_{hg^{-1}})_{h\\in H,g\\in G}$, where $x_g$ ($g\\in G$) are indeterminates indexed by the elements in $G$. Then, we define an invariant $\\Theta(G,H)$ for a given pair $(G,H)$ by the $k$-wreath determinant of the matrix $X$, where $k$ is the index of $H$ in $G$. The $k$-wreath determinant of $n$ by $kn$ matrix is a relative invariant of the left action by the general linear group of or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2425","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"}