{"paper":{"title":"Some Quantitative Characterizations of Certain Symplectic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. R. Moghaddamfar, M. Akbari","submitted_at":"2013-04-27T07:37:18Z","abstract_excerpt":"Given a finite group $G$, denote by ${\\rm D}(G)$ the degree pattern of $G$ and by ${\\rm OC}(G)$ the set of all order components of $G$. Denote by $h_{{\\rm OD}}(G)$ (resp. $h_{{\\rm OC}}(G)$) the number of isomorphism classes of finite groups $H$ satisfying conditions $|H|=|G|$ and ${\\rm D}(H)={\\rm D}(G)$ (resp. ${\\rm OC}(H)={\\rm OC}(G)$). A finite group $G$ is called OD-characterizable (resp. OC-characterizable) if $h_{\\rm OD}(G)=1$ (resp. $h_{\\rm OC}(G)=1$). Let $C=C_p(2)$ be a symplectic group over binary field, for which $2^p-1>7$ is a Mersenne prime. The aim of this article is to prove that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7343","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"}