{"paper":{"title":"Class-preserving automorphisms of finite $p$-groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Manoj K. Yadav","submitted_at":"2014-06-28T07:19:09Z","abstract_excerpt":"Let $G$ be a finite group minimally generated by $d(G)$ elements and $\\Aut_c(G)$ denote the group of all (conjugacy) class-preserving automorphisms of $G$. Continuing our work [Class preserving automorphisms of finite $p$-groups, J. London Math. Soc. \\textbf{75(3)} (2007), 755-772], we study finite $p$-groups $G$ such that $|\\Aut_c(G)| = |\\gamma_2(G)|^{d(G)}$, where $\\gamma_2(G)$ denotes the commutator subgroup of $G$. If $G$ is such a $p$-group of class $2$, then we show that $d(G)$ is even, $2d(\\gamma_2(G)) \\le d(G)$ and $G/\\Z(G)$ is homocyclic. When the nilpotency class of $G$ is larger tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7365","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"}