{"paper":{"title":"The Answers to a Problem and Two Conjectures about OD-Characterization of Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Mahmoudifar, Behrooz Khosravi","submitted_at":"2014-09-28T13:01:29Z","abstract_excerpt":"In [Akbari and Moghaddamfar, Recognizing by order and degree pattern of some projective special linear groups, {\\it Internat. J. Algebra Comput.}, 2012] the authors possed the following problem: \\\\ {\\bf Problem.} {\\it Is there a simple group which is $k$-fold OD-characterizable for $k\\geq3\\ ?$ }\n  In this paper as the main result we give positive answer to the above problem and we introduce two simple groups which are $k$-fold OD-characterizable such that $k\\geq6$.\n  Also in [R. Kogani-Moghadam and A. R. Moghaddamfar, Groups with the same order and degree pattern, {\\it Science China Mathematic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7903","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"}