{"paper":{"title":"Classification of finite C{\\theta}{\\theta}-groups with even order and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Mahmoudifar","submitted_at":"2017-03-02T06:40:08Z","abstract_excerpt":"A finite group of order divisible by 3 in which centralizers of 3-elements are 3-subgroups will be called a C{\\theta}{\\theta}-group. The prime graph (or Gruenberg-Kegel graph) of a finite group G is denoted by {\\Gamma}(G) (or GK(G)) and its a familiar. Also the degrees sequence of {\\Gamma}(G) is called the degree pattern of G and is denoted by D(G). In this paper, first we classify the finite C{\\theta}{\\theta}-groups with even order. Then we show that there are infinitely many C{\\theta}{\\theta}-groups with the same degree pattern. Finally, we proved that the simple group PSL(2, q) and the almo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00635","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"}