{"paper":{"title":"Finite $p$-groups of class 3 with noninner automorphisms of order $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Abdollahi, Mohsen Ghoraishi","submitted_at":"2011-10-31T18:31:15Z","abstract_excerpt":"A longstanding conjecture asserts that every non-abelian finite $p$-group $G$ admits a non-inner automorphism of order $p$. The conjecture is valid for finite $p$-groups of class 2. Here, we prove every finite non-abelian $p$-group $G$ of class 3 with $p>2$ has a noninner automorphism of order $p$ leaving $\\Phi(G)$ elementwise fixed. We also prove that if $G$ is a finite 2-group of class 3 which cannot be generated by 4 elements, then $G$ has a non-inner automorphism of order 2 leaving $\\Phi(G)$ elementwise fixed. We also prove that the latter conclusion holds for finite 2-groups $G$ of class "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6888","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"}