{"paper":{"title":"Finite Groups with Submultiplicative Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"H. Radjavi, L. Grunenfelder, M. Omladi\\v{c}, T. Ko\\v{s}ir","submitted_at":"2011-09-09T07:12:28Z","abstract_excerpt":"We study abstract finite groups with the property, called property $\\hat{s}$, that all of their subrepresentations have submultiplicative spectra. Such groups are necessarily nilpotent and we focus on $p$-groups. $p$-groups with property $\\hat{s}$ are regular. Hence, a 2-group has property $\\hat{s}$ if and only if it is commutative. For an odd prime $p$, all $p$-abelian groups have property $\\hat{s}$, in particular all groups of exponent $p$ have it. We show that a 3-group or a metabelian $p$-group ($p \\ge 5$) has property $\\hat{s}$ if and only if it is V-regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1916","kind":"arxiv","version":2},"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"}