{"paper":{"title":"Elementary proof that $\\mathbb Z_p^4$ is a DCI-group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Joy Morris","submitted_at":"2014-03-18T18:11:03Z","abstract_excerpt":"A finite group $R$ is a DCI-group if, whenever $S$ and $T$ are subsets of $R$ with the Cayley graphs ${\\rm Cay}(R,S)$ and ${\\rm Cay}(R,T)$ isomorphic, there exists an automorphism $\\varphi$ of $R$ with $S^\\varphi=T$.\n  Elementary abelian groups of order $p^4$ or smaller are known to be DCI-groups, while those of sufficiently large rank are known not to be DCI-groups. The only published proof that elementary abelian groups of order $p^4$ are DCI-groups uses Schur rings and does not work for $p=2$ (which has been separately proven using computers). This paper provides a simpler proof that works "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4557","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"}