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A family of nonnormal Cayley digraphs. (Chinese. English summary) Zbl 1025.05031

Summary: We call a Cayley digraph \(\Gamma= \text{Cay}(G,S)\) normal for \(G\) if \(G_R\), the right regular representation of \(G\), is a normal subgroup of the full automorphism group \(\operatorname{Aut}(\Gamma)\) of \(\Gamma\). In this paper we determine the normality of Cayley digraphs of valency 2 on non-abelian groups of order \(2p^2\) (\(p\) odd prime). As a result, a family of nonnormal Caylay digraphs is found.

MSC:

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