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Some new groups which are not CI-groups with respect to graphs. (English) Zbl 1380.05201
Summary: A group \(G\) is a CI-group with respect to graphs if two Cayley graphs of \(G\) are isomorphic if and only if they are isomorphic by a group automorphism of \(G\). We show that an infinite family of groups which include \(D_n\times F_{3p}\) are not CI-groups with respect to graphs, where \(p\) is prime, \(n \neq 10\) is relatively prime to \(3p\), \(D_n\) is the dihedral group of order \(n\), and \(F_{3p}\) is the nonabelian group of order \(3p\).

MSC:
05E18 Group actions on combinatorial structures
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
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