An elementary Abelian group of rank 4 is a CI-group

DOI10.1006/jcta.2000.3140zbMath1002.20030OpenAlexW2076765371MaRDI QIDQ5937246

Mikhail E. Muzychuk, Mitsugu Hirasaka

Publication date: 16 January 2002

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.2000.3140

zbMATH Keywords

finite groupsSchur ringsCayley isomorphism propertyCI-groupselementary Abelian groups

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite abelian groups (20K01)

Related Items (28)

On the isomorphism problem for Cayley graphs of abelian groups whose Sylow subgroups are elementary abelian or cyclic ⋮ Normal Cayley digraphs of cyclic groups with CI-property ⋮ Enumeration of cubic Cayley graphs on dihedral groups ⋮ On Schur rings over infinite groups ⋮ Further restrictions on the structure of finite DCI-groups: an addendum ⋮ CI-property of \(C_p^2 \times C_n\) and \(C_p^2 \times C_q^2\) for digraphs ⋮ Elementary Abelian \(p\)-groups of rank \(2p+3\) are not CI-groups. ⋮ Enumerating Cayley (di-)graphs on dihedral groups ⋮ Further restrictions on the structure of finite CI-groups ⋮ Elementary abelian \(p\)-groups of rank greater than or equal to \(4p-2\) are not CI-groups. ⋮ Monomial isomorphisms of cyclic codes ⋮ The CI problem for infinite groups ⋮ On the existence of self-complementary and non-self-complementary strongly regular graphs with Paley parameters ⋮ Supercharacter Theory Constructions Corresponding to Schur Ring Products ⋮ Elementary abelian groups of rank 5 are DCI-groups ⋮ An answer to Hirasaka and Muzychuk: every \(p\)-Schur ring over \(C_p^3\) is Schurian. ⋮ On a conjecture of Spiga ⋮ The Cayley isomorphism property for \(\mathbb{Z}_p^3\times\mathbb{Z}_q\) ⋮ On isomorphisms of abelian Cayley objects of certain orders ⋮ CI-property of elementary abelian 3-groups ⋮ Unnamed Item ⋮ The group \(C_p^4 \times C_q\) is a DCI-group ⋮ The Group is a CI-Group ⋮ Schur rings. ⋮ The Cayley isomorphism property for the group C^5_2 × C_p ⋮ The Cayley isomorphism property for the group C4×Cp2 ⋮ Elementary proof that \(\mathbb{Z}_p^4\) is a DCI-group ⋮ Onp-Schur Rings Over Abelian Groups of Orderp³

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