{"paper":{"title":"A note on commuting automorphisms of some finite $p$-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Deepak Gumber, Sandeep Singh","submitted_at":"2015-06-16T03:10:59Z","abstract_excerpt":"An automorphism $\\alpha$ of a group $G$ is called a commuting automorphism if each element $x$ in $G$ commutes with its image $\\alpha(x)$ under $\\alpha$. Let $A(G)$ denote the set of all commuting automorphisms of $G$. Rai [Proc. Japan Acad., Ser. A {\\bf 91} (2015), no. 5, 57-60] has given some sufficient conditions on a finite $p$-group $G$ such that $A(G)$ is a subgroup of Aut$(G)$ and, as a consequence, has proved that in a finite $p$-group $G$ of co-class 2, where $p$ is an odd prime, $A(G)$ is a subgroup of Aut$(G)$. We give here very elementary and short proofs of main results of Rai."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05989","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"}