{"paper":{"title":"A characterization of A_5 by its Same-order type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"L. Jafari Taghvasani, M. Zarrin","submitted_at":"2015-12-27T13:13:15Z","abstract_excerpt":"Let G be a group, define an equivalence relation s as below: 8 g; h 2 G g s h () jgj = jhj the set of sizes of equivalence classes with respect to this relation is called the same-order type of G. Shen et al. (Monatsh. Math. 160 (2010), 337-341.), showed that A5 is the only group with the same-order type f1; 15; 20; 24g. In this paper, among other things, we prove that a nonabelian simple group G has same-order type fr; m; n; kg if and only if G ?= A5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08215","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"}