{"paper":{"title":"On finite $p$-groups whose central automorphisms are all class preserving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Manoj K. Yadav","submitted_at":"2012-08-15T07:15:50Z","abstract_excerpt":"We obtain certain results on a finite $p$-group whose central automorphisms are all class preserving. In particular, we prove that if $G$ is a finite $p$-group whose central automorphisms are all class preserving, then $d(G)$ is even, where $d(G)$ denotes the number of elements in any minimal generating set for $G$. As an application of these results, we obtain some results regarding finite $p$-groups whose automorphisms are all class preserving. In particular, we prove that if $G$ is a finite $p$-groups whose automorphisms are all class preserving, then order of $G$ is at least $p^8$ and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3046","kind":"arxiv","version":3},"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"}