The Group is a CI-Group

DOI10.1080/00927870802504957zbMath1211.05079OpenAlexW2045459515MaRDI QIDQ3646334

István Kovács, Mikhail E. Muzychuk

Publication date: 20 November 2009

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870802504957

zbMATH Keywords

Schur ringsCI-groupsCayley graph isomorphism

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Algebraic combinatorics (05E99) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (16)

On isomorphisms of vertex-transitive graphs ⋮ ON ISOMORPHISMS OF VERTEX-TRANSITIVE CUBIC GRAPHS ⋮ 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 ⋮ Generalized dihedral CI-groups ⋮ On the Cayley isomorphism problem for Cayley objects of nilpotent groups of some orders ⋮ 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 ⋮ Enumerating Cayley (di-)graphs on dihedral groups ⋮ Recognizing and Testing Isomorphism of Cayley Graphs over an Abelian Group of Order 4p in Polynomial Time ⋮ The Cayley isomorphism property for \(\mathbb{Z}_p^3\times\mathbb{Z}_q\) ⋮ Unnamed Item ⋮ The group \(C_p^4 \times C_q\) is a DCI-group ⋮ The Cayley isomorphism property for the group C^5_2 × C_p ⋮ The Cayley isomorphism property for the group C4×Cp2 ⋮ Normal Cayley digraphs of generalized quaternion groups with CI-property

Cites Work

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• Coherent algebras
• Corrigendum to: On Ádám's conjecture for circulant graphs
• On isomorphisms of finite Cayley graphs---a survey
• An elementary abelian group of large rank is not a CI-group
• Ádám's conjecture is true in the square-free case
• ABELIAN SUBGROUPS OF SIMPLY PRIMITIVE GROUPS OF DEGREE p³, WHERE p IS PRIME
• Graphs with circulant adjacency matrices
• CRESTED PRODUCTS OF ASSOCIATION SCHEMES
• An elementary Abelian group of rank 4 is a CI-group

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