Elementary abelian \(p\)-groups of rank greater than or equal to \(4p-2\) are not CI-groups.

DOI10.1007/s10801-007-0059-2zbMath1129.05018OpenAlexW2080359665MaRDI QIDQ2458252

Pablo Spiga

Publication date: 31 October 2007

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10801-007-0059-2

zbMATH Keywords

Cayley graphSchur ringCI-group2-closure

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Directed graphs (digraphs), tournaments (05C20)

Related Items (12)

On isomorphisms of vertex-transitive graphs ⋮ ON ISOMORPHISMS OF VERTEX-TRANSITIVE CUBIC GRAPHS ⋮ Normal Cayley digraphs of cyclic groups with CI-property ⋮ Normal Cayley digraphs of dihedral groups with CI-property ⋮ Elementary Abelian \(p\)-groups of rank \(2p+3\) are not CI-groups. ⋮ On the maximum order of nilpotent transitive permutation groups. ⋮ The CI problem for infinite groups ⋮ Elementary abelian groups of rank 5 are DCI-groups ⋮ On a conjecture of Spiga ⋮ CI-property of elementary abelian 3-groups ⋮ Elementary proof that \(\mathbb{Z}_p^4\) is a DCI-group ⋮ Normal Cayley digraphs of generalized quaternion groups with CI-property

Uses Software

• GAP

Cites Work

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• A non-Cayley-invariant Cayley graph of the elementary Abelian group of order 64
• On isomorphisms of finite Cayley graphs---a survey
• An elementary abelian group of large rank is not a CI-group
• Isomorphism problem for a class of point-symmetric structures
• An elementary Abelian group of rank 4 is a CI-group

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