{"paper":{"title":"Elements with r-th roots in finite groups","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Elaheh Khamseh (Islamic Azad University, Farshid Saeedi (Islamic Azad University, Francesco G. Russo (Universita' degli Studi di Palermo, Iran), Italy), Mashhad, Mohammed Reza R. Moghaddam (Ferdowsi University of Mashhad, Palermo","submitted_at":"2010-08-12T06:51:48Z","abstract_excerpt":"The probability that a randomly chosen element of a finite group is an $r$--th root (for any integer $r\\geq2$) has been studied largely in case $r=2$. Certain techniques may be generalized for $r>2$ and here we find the exact value of this probability for projective special linear groups. A result of density is placed at the end, in order to show an analogy with the case $r=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2055","kind":"arxiv","version":4},"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"}