{"paper":{"title":"Simple twisted group algebras of dimension $p^4$ and their semi-centers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Ofir Schnabel","submitted_at":"2014-12-08T09:23:23Z","abstract_excerpt":"For simple twisted group algebra over a group $G$, if $G^{\\shortmid}$ is Hall subgroup of $G$ then the semi-center is simple. Simple twisted groups algebras correspond to groups of central type. We classify all groups of central type of order $p^4$ where $p$ is prime and use this to show that for odd primes $p$ there exists a unique group $G$ of order $p^4$ such that there exists simple twisted group algebra over $G$ with a commutative semi-center. Moreover, if $1< |G|< 64$, then the semi-center of simple twisted group algebras over $G$ is non-commutative and this bounds are strict."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2490","kind":"arxiv","version":4},"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"}