Elementary Abelian \(p\)-groups of rank \(2p+3\) are not CI-groups.

DOI10.1007/S10801-011-0273-9zbMath1294.20069arXiv0911.2991OpenAlexW2037896424MaRDI QIDQ644693

Gábor Somlai

Publication date: 7 November 2011

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

Full work available at URL: https://arxiv.org/abs/0911.2991

zbMATH Keywords

Cayley graphsCI-groupselementary Abelian \(p\)-groups

Mathematics Subject Classification ID

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

Related Items (14)

On isomorphisms of vertex-transitive graphs ⋮ ON ISOMORPHISMS OF VERTEX-TRANSITIVE CUBIC GRAPHS ⋮ Normal Cayley digraphs of cyclic groups with CI-property ⋮ Generalized dihedral CI-groups ⋮ Normal Cayley digraphs of dihedral groups with CI-property ⋮ CI-property of \(C_p^2 \times C_n\) and \(C_p^2 \times C_q^2\) for digraphs ⋮ Some new groups which are not CI-groups with respect to graphs ⋮ The CI problem for infinite groups ⋮ Elementary abelian groups of rank 5 are DCI-groups ⋮ The Cayley isomorphism property for \(\mathbb{Z}_p^3\times\mathbb{Z}_q\) ⋮ The group \(C_p^4 \times C_q\) is a DCI-group ⋮ The Cayley isomorphism property for the group C^5_2 × C_p ⋮ Elementary proof that \(\mathbb{Z}_p^4\) is a DCI-group ⋮ Normal Cayley digraphs of generalized quaternion groups with CI-property

Cites Work

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• CI-property of elementary abelian 3-groups
• A non-Cayley-invariant Cayley graph of the elementary Abelian group of order 64
• On isomorphisms of finite Cayley graphs
• An elementary abelian group of large rank is not a CI-group
• Elementary abelian \(p\)-groups of rank greater than or equal to \(4p-2\) are not CI-groups.
• An elementary Abelian group of rank 4 is a CI-group

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