{"paper":{"title":"On the tensor degree of finite groups","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.GR","authors_text":"Damghan, Francesco G. Russo (Universita' degli Studi di Palermo, Iran), Italy), Palermo, Peyman Niroomand (Damghan University","submitted_at":"2013-03-06T15:51:12Z","abstract_excerpt":"We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \\otimes y= 1_{_{G \\otimes G}}$ in the nonabelian tensor square $G \\otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1364","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"}