{"paper":{"title":"$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Abdollahi, S. Mohsen Ghoraishi","submitted_at":"2013-07-20T12:33:27Z","abstract_excerpt":"An automorphism of a group is called outer if it is not an inner automorphism.\n  Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\\phi$ of $G$ the subgroup $C_G(\\phi)=\\{x\\in G \\;|\\; x^\\phi=x\\}$ has order $p$ if and only if $G$ is of order at most $p^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5417","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"}